Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7 th Grade Mathematics Additional Problems 1. Express each expression mathematically. a. 7 more than the product of a number and 5 b. 4.5 fewer than the quotient of a number and 8 c. The quotient of -10 and the difference of a number and 8 d. One fourth of the difference of 15 and a quantity e. The total of the product of 2 and a number and 7 and a different number 2. Determine the correct mathematical operation by identifying words that indicate addition, subtraction, multiplication, and division. Underline the word(s) indicating the operation, then write and simplify a numerical expression using that operation. Attend to precision as you include labels in your problem solving. a. What is the combined length of these three fence lines? 105 ft, 290 ft, and 756 ft. b. When at the North Towne Mall, Jill saw a jacket she wanted for $65. At another store, the asking price was twice as much. How much was the jacket at the other store? c. Last month Ray’s production line made 14,566 water valves. This month his line made13,880. What was the decrease in the amount of water valves made? d. At a meeting, Daryl stated that by the end of next year, international sales will be four times higher than today. If international sales are $1,200,000 this year, what will they be next year? e. If 3.25 lbs of gold are divided evenly among 4 pirates, how much gold will each pirate get?
Transcript
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems1. Express each expression mathematically.
a. 7 more than the product of a number and 5b. 4.5 fewer than the quotient of a number and 8c. The quotient of -10 and the difference of a number and 8d. One fourth of the difference of 15 and a quantitye. The total of the product of 2 and a number and 7 and a different number
2. Determine the correct mathematical operation by identifying words that indicate addition, subtraction, multiplication, and division. Underline the word(s) indicating the operation, then write and simplify a numerical expression using that operation. Attend to precision as you include labels in your problem solving.a. What is the combined length of these three fence lines? 105 ft, 290 ft, and 756 ft.b. When at the North Towne Mall, Jill saw a jacket she wanted for $65. At another store, the asking price was twice as much. How much was the jacket at the other store?c. Last month Ray’s production line made 14,566 water valves. This month his line made13,880. What was the decrease in the amount of water valves made?d. At a meeting, Daryl stated that by the end of next year, international sales will be four times higher than today. If international sales are $1,200,000 this year, what will they be next year?e. If 3.25 lbs of gold are divided evenly among 4 pirates, how much gold will each pirate get?f. What is the total weight of twenty-five, 10.5 lb packages?g. A holiday party of 45 guests is to be served by Speedy Catering Service. If each guest is to receive a 6 oz portion of ribeye steak, how many ounces of ribeye should Speedy Catering order for the party?h. If you are told, “I want you to increase the length of time that casserole stays in the oven by 10 minutes more than what the recipe says (45 minutes).” How long will you keep the casserole in the oven?
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problemsi. If a 7 acre parcel of land is split-up into 20 equal sized lots, how large will each lot be? j. My checkbook has a balance of $350. If I then write a check for $78.50, how much money remains in my checkbook account?k. It takes John about 0.3 hr to interview a candidate for a new job. In an 8 hr work day, how many people could John interview per day?
3. What is the sum of 8 and a number if the number is negative eleven?4. What is twice the number y if y =3
4 ?Need Help? Check out these related resources. Learnzillion: Read and Write an Algebraic Expression Containing a Variable
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5. Are the following expressions equivalent? Justify your answer.−2 (3+6 )+5 and −8−1
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems6. Describe the mistakes in the following problems and correct the students’ work.
a. b.
7. “What a Mess!”Alex finished his homework last night and left it on the kitchen counter. His little sister accidentally splashed tomato sauce on it. Help Alex to figure out what values have been covered up by sauce spatter spots.a.b.C.d.
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Learnzillion: Solve Multiplication Problems by Using the Distributive Propertyhttp://learnzillion.com/lessons/702-solve-multiplication-problems-by-using-the-distributive-property8. Are the following expressions equivalent? Justify your answer.
10. What are the factors of each expression below?a. 18xb. 32cc. 7bd. 100m
11. What are the common factors for each of the pairs of expressions below? Identify the greatest common factor of each pair.a. 18x & 32b. 9n & 12xc. 9t & 7td. 14v & 8v
12. Write the expressions in their factored form.a. 3x + 9b. 4m + 2c. 14y + 21d. 5d + 7e. 4c + 3 + 5c + 9
13. Are the following expressions equivalent? Justify your answer.a. 5 – 3x – 7 and -3(4 + x)b. -8(2w – 1) and 8 – 16wc. –h + 8 – 3h and -4 ( h + 2)d. 2(3w – 2) and 6w−205
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
14. Write the expressions in their simplest form.a. 3
5(r−10 )+ 2
5r
b. 12c+102
−c+7c. 7−0.2(−6+h)d. 30−(3a−1 )e. −18 y−248f. 2 [15−3 ( x−9 ) ]15. What are the factors of each expression below?a. -9wb. -24yc. -5h
16. What are the common factors for each of the pairs of expressions below? Identify the greatest common factor of each pair.a. -20x & 30b. 15n & -12xc. -18t & -3td. 4v & -v17. Write the expressions in a factored form.a. 2x – 10b. -6m + 2c. -16y – 12d. -5d + 9e. 20w – 6
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Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems Learnzillion: Factor an Expressionhttp://learnzillion.com/lessons/809-factor-an-expression Learnzillion: Simplify Expressions Using Distribution and Combining Like Termshttp://learnzillion.com/lessons/810-simplify-expressions-using-distribution-and-combining-like-terms Learnzillion: Simplify an Expression with a Fraction Using the Distributive Propertyhttp://learnzillion.com/lessons/811-simplify-an-expression-with-a-fraction-using-the-distributive-property Learnzillion: Simplify an Expression with a Fraction by Adding or Subtracting Terms with Fractionshttp://learnzillion.com/lessons/812-simplify-an-expression-with-a-fraction-by-adding-or-subtracting-terms-with-fractions
18. Write the expressions in their simplest form, if possible.a. 8h2+9−h+6h2−3h−10
b. 12
(4 r2−10 r )−r+5
c. 7 g2+8−g−(−2 )−g2
d. 15x (2x−8 )3e. 8 x−2 x (−5+x)f. (8−c )−(3c−1 )
g. −12 y2−26 y419. What are the factors of each expression below?
a. 8x2 b. -15y c. 6w3
20. What are the common factors for each of the pairs of expressions below? Identify the greatest common factor of each pair.a. 14w2 & 21w b. 5n & -12n2c. -8t & -10t d. 16v2 & -v2
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems21. Write the expressions in a factored form.
a. 2x2 – 10x b. -8m2 + 20c. -10y – 12y2 d. -d + 9d2e. 14w – 6
22. Look at each expression. Is it equivalent to 36x + 24y? Justify your answers.A. 6(6 x+4 y ) B. 30(6 x−6 y) C. 12(x+2 y+2x )
23. An equilateral triangle has a perimeter of 6x+15. What is the length of each side of the triangle?24. Emilie says the two expressions 2(3a - 2) + 4a and 10a – 2 are equivalent. Is she correct? Explain why or why not.25. Look at each expression. Is it equivalent to x+3 y
2 ? Justify your answers.A. 4 x+3 y
8 B. 54( 2 x+6
5)
C. 12(x+3 y ) D. 2
3( 5 x
6+ 9 y
4− x
12)
26. What is the length and width of the rectangle below?
27. If we multiply x2 + 34 by 4, we get 2x+3. Is 2x+3 an equivalent expression x2 + 3
4 ?28. Write an expression for the sequence of operations.
a. Add 3 to x, subtract the result from 1, then double what you have.b. Add 3 to x, double what you have, then subtract 1 from the result.
4b2a
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems29. Multiple Choice Question: Justify your choice.
When 58x+1 1
3 is subtracted from 1 14x−5 1
6 , the result is:a) 5
8x−3 5
6
b) 58x−6 1
2
c) −58x+3 5
6
d) −58x+6 1
2
30. In the following expressions, a & b are both integers.a (3x−8) is equivalent to b−18 x.
What is the value of a? What is the value of b?31. Review:A scale drawing for a construction project uses a scale of 1 inch = 4 feet. The dimensions of the rectangular family room on the scale drawing are 7.5 inches by 12 inches.What will be the actual area of the floor of the family room after the construction project is completed?32. Review:David is making his own strawberry yogurt. In David’s mixture, the number of strawberries is proportional to the amount of milk, in cups. David uses 4 cups of milk for every 14 strawberries in his mixture. Which equation represents the relationship between s, the number of strawberries, and m, the number of cups of milk he uses?33. Review:Simplify the following numerical expression, without a calculator. Show your work.
56−2
3 (6−12 )+ 3
4
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems34. The students in Mr. Sanchez’s class are converting distance measured in miles to kilometers. To estimate the number of kilometers Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato first divides the number of miles by 5, then multiplies the result by 8.
a. Write an algebraic expression for each method.b. Use your answer to part (a) to decide if the 2 methods are equivalent.35. All books in a store are being discounted by 30%. Let x represent the regular price of any book in the store. Write an expression that can be used to find the sale price of any book in the store.36. Damian plans to do a lot of babysitting this summer. He charges $6.50 per hour and usually babysits for 3 hours. He has agreed to babysit every Saturday from mid-June through August (10 times) for his neighbors.Damian’s parents said that they would split the cost of a new computer with him. Its costs $500 and he has to save half that amount before school starts.
a. How much money will Damian earn from the babysitting he already has scheduled? b. How much more money will he need to make a total of $250?c. How many hours will he have to babysit to earn the extra money he needs?d. How much more would Damian have to charge per hour if he wanted to make the whole $250, in the number of hours he already has scheduled to babysit?e. If Damian wants to do a combination of raising his prices and working more hours, would that work? How could he do it and raise the $250 he needs?37. Holly and Aubrey are having a party. They plan to serve lemonade. Including the two girls, there will be 14 guests at the party. Holly and Aubrey are assuming that each person will have a cup of lemonade.
a. How many cups of lemonade do Holly and Aubrey need for their party?b. How many quarts of lemonade is that?
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problemsc. How many quart pitchers would Holly and Aubrey need to store and serve the lemonade?d. How many gallons of lemonade do the number of cups equal?e. How many gallon pitchers would Holly and Aubrey need to store and serve the lemonade?f. Which is the better size to use – quart or gallon? Explain your reasoning.
38. A school bus can take 24 students on a field trip. Write an expression that gives the number of students that can go on a field trip if there are b buses.a. Show how you can use the expression to find the number of students that can go on the trip if there are 12 buses.b. How many buses are need to take 216 students on the trip? Explain.
39. Omani wants to place a computer 24 12 inches long in the center of a table 28 3
4 wide. About how far from the edge will you place the computer?40. Brian earns $45 per day at his job. He gets a 10% increase. He works 24 days in month. How much more money will he get for the month?
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41. Which would have a greater distance around the outside a square with a side length of 4 inches or a circle with a diameter of 4 inches? Justify your answer.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems42. If a car tire has a 10 inch radius, how far does it travel in one revolution of the tire?43. Review: Simplify each of the following expressions.
a. 4 ( x+7 )−5 b. 3−4 12(2−x)
c. −2 x (3x+4) d. −3 x+603e. 5.2a2−4.6a+2.1+0.5 (a−3)
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44. An artist used a silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest circle that could fit in the square, as shown at right. How many more inches of silver wire did the artist use compared to the copper wire? Show all work necessary to justify your response.45. The seventh grade class is building a mini-golf game for the school carnival. The end of the putting green will be a circle. If the circle is 10 feet in diameter, how many square feet of grass carpet will they need to buy to cover the circle? 46. If a circle is cut from the square piece of plywood at right, how much plywood would be leftover? Show your work necessary to justify your response.47. Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, which he finds to nearest millimeter, to be 5 centimeters.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problemsa. How large is the possible error in Juan’s measurement of the diameter of the circle? Explain.b. As a percentage of the diameter, how large is the possible error in Juan’s measurement?c. To find the area of the circle, Juan uses the formula A=π r2 where A is the area of the circle and r is its radius. He uses 3.14 for π. What value does Juan get for the area of the circle?d. As a percentage, how large is the possible error in Juan’s measurement of the circle?
48. What is the perimeter of the inside of the track?
49. The figure below is composed of eight circles, seven small circles and one large circle containing them. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.a. What is the area of the large circle?b. What is the area of the shaded part of the figure?Need Help? Check out these related resources.
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Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
50. You thought the balance in your checkbook was $53, but when your bank statement arrived, you realized that you forgot to record a check. The bank statement lists your balance as $47. Let x represent the value of the check that you forgot to record. Which equation is a correct model for the situation? Defend your choice and then solve the correct equation.A. 53−x=47 B. x−47=53
51 – 53: Match the real-life problem with an equation. Then solve the problem.A. x+15=7 B. 15−x=7 C. 15+7=x D. x+15=−7
51. You own 15 CDs. You buy 7 more. How many CDs do you own now?52. There are 15 members of a high school band brass section. After graduation there are only 7 members. How many members graduated?53. The temperature rose 15 degrees to 7℉. What was the original temperature?
54. Oh no! Georgia was working on her homework. She noticed that her little sister spilled pizza in the middle of the problem. She knows that the answer is correct, but can’t remember what the original problem was. Her Algebra teacher will not accept homework with pizza spilled on it and she must recopy the problem on a new sheet of paper. Help Georgia figure out what the missing number is.55. Write an equation to find the length of the side marked by x. Solve the equation. (Show your work.) The perimeter is 43 centimeters.
x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15x + = 12 x = 15
70 ft2
15 cm
8 cm x
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems56. Turner Field in Atlanta, Georgia has 49,598 seats. Progressive Field in Cleveland Ohio, has 43, 429 seats. How many seats need to be added to Progressive Field for it to have as many seats as Turner Field? Write and solve an equation to find your answer. Explain your equation solving strategy.
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57 – 58: Write an equation to find the length of the side marked by x. Solve the equation.57. The area is 24 m2. 58. The area of largest triangle is 30 cm2.
59. A homeowner is installing a fence around the garden at the right. The garden has a perimeter of 220 feet. Write and solve an equation to find the garden’s dimensions.60. The perimeter of the square is 20 feet. Write an equation to find the length of the side marked by x. Solve the equation.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems61. Which equations are equivalent?
I. 35x=3 II. x5=2 III. 2 x=10 IV. −x=−5
62. Which are possible ways to describe how to solve -8y = 40 in one step?A. Divide each side by 40B. Multiply each side by -8C. Divide each side by -8D. Add 8 to each sideE. Multiply each side by −1
8F. Divide each side by 863. Create an equation that would be solved using the method described. Solve the equation. Check your solution.A. Divide both sides by 4.B. Multiply both sides by -7C. Multiply both sides by 2
3D. Divide both sides by 1.4Need Help? Check out these related resources.
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64. Twelve is less than 3 times another number can be shown by the inequality 12 < 3n. What numbers could possible make this a true statement?65. The class must raise at least $100 to go on the field trip. They have collected $20. Write (and solve, if necessary) an inequality to represent the amount of money, m, the class still needs to raise. Represent this inequality on a number line.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems66. An inequality is shown.
x>4Select the statement(s) and number line(s) that can be represented by the inequality. a. The temperature increased by 4 degrees Fahrenheit.b. The value of a number substituted for x is greater than 4.c. Marcus drinks more than 4 glasses of water every day.d.
e.67. Select the equation(s)/situation(s) where x=5 is a solution. Justify your choice(s).a. 2x + 4 = 14b. 5x = 55c. Anna’s brother is at least 4 feet tall. Let x represent Anna’s brother’s height, in feet.d. 6x + 3=14e. 2 x≥−10f. 8 + 3x=23g. 6x = 30h. x−6←1i. 5x = 1j. −x>−4
68. Review: Are 4 (3 x− y ) and 12 x−4 y equivalent expressions? Why or why not?69. Review: Circles
a. The circumference of a circle is 56.5 meters. What is the diameter of the circle?b. The circumference of a circle is 47 feet. What is the radius of the circle?c. The circumference of a circle is 63 inches. What is the area of the circle?
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Khan Academy: Using Multiplication and Division(Note: Don’t worry about being able to do the “set notation” discussion – but it’s good to hear.)http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division
70. Try to solve each situation first without writing an equation, then secondly by writing and solving an algebraic equation that could represent the situation. a. You are at a restaurant and are paying the entire bill for your group.
i. The bill is $35.62. You want to leave the waitress a 15% tip. What is your total cost?ii. The total cost that you paid was $51. You had left a 20% tip for the waitress. What was the price of the bill before the tip?iii. The bill was $52.75. Your total cost was $59.08. How much did you leave for a tip? What percent did you leave for a tip?b. You are working with a rectangle.
i. The perimeter of the rectangle is 65 inches and the width is 14. What is the length?ii. The length of a rectangle is 14 cm and the width is 2 cm less than the length. What is the perimeter?
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problemsiii. The length of a rectangle is 5 inches more than the width. The perimeter of the rectangle is 130 inches. Find the length and width of the rectangle.
c. You are traveling to a friend’s house that is 8 miles away.i. You walk the distance at a rate of 3 miles per hour. How long did it take you to get to your friend’s house?ii. You decided to ride your bike next time and it took you 32 minutes. At what speed (rate) were you riding your bike?iii. You rode your bike to your friend’s house then both of you rode to the movie theater at a rate of 16 miles per hour. You found that you had ridden you bike for a total of 12 miles. How long did it take you to ride from your friend’s house to the movie theater?
71. Simple InterestThe formula for finding the amount of “simple” interest earned (or owed) can be calculated using the following formula:
For example, Sara deposited $4,500 at 9.5% for 6 years. To the find the amount of interest Sara will earn at the end of those 6 years, we use the formula…
I = P r tWhere… I = the amount of interest; P = the principal amount; r = the rate at which interest is accrued; and t = the amount of time since the Principal amount was deposited/borrowed
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional ProblemsI = P r t → Interest Sara will earn =
$4,500 •9.5 % •6=$ 4,500 • 9.5100
•6=$ 2565.00
Using the simple interest formula, answer the following questions:a. If Lloyd deposits $3,000 at 3.5% for 5 years and Renee deposits $2,500 at 4.5% for 5 years, who will earn more interest? How much more will he or she earn? b. If Jenn wants to deposit her $200 birthday check at an interest rate of 3%, how long will she need to wait before she earns $40 in interest? How long will she need to wait before she earns $100 in interest?c. Jeremie deposited $400 10 years ago at an interest rate of 3.75%. How much money is in the account now?d. How much would Xao need to deposit if he would like to earn $25 in interest, at an interest rate of 2% after 5 years?e. Janet wants to deposit the $500 she earned babysitting this summer. Her goal is to earn $50 in interest over a period of 6 years. What interest rate will she need to find in order to meet her goal?Need Help? Check out these related resources.
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Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
72. A rectangle has a perimeter of at least 42 centimeters. The width is 4 centimeters less than the length. What are all the possible lengths of the rectangle? State 3 length and width combinations that could represent this rectangle.73. A Ferris wheel is set up at a county fair. The passengers travel about 408 feet in one revolution of the wheel. What is the area of the Ferris wheel?74. You want to hang 3 equally-sized travel posters on the wall in your room so that the posters on the ends are each 3 feet from the end of the wall. The wall is 13.5 feet long. The posters are each 2 feet wide. You want the spacing between the posters to be equal. How much space should you leave between the posters?75. The largest tree in the United States is growing in Sequoia National Park in California. The tree is a giant sequoia whose truck is roughly circular and has a circumference of 998 inches. What is the tree’s cross sectional area? 76. The perimeter of the triangle is 24 feet. Find the length of each side.
77. Find, describe, and correct the error in solving the equation.x + 4
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems78. Solve the following open ended statements for the given variable. Show your work. Check your solution(s).
79. Review: A farmer tied his cow, Bessy, to a post with a rope 5 meters long. a. How many square meters of grazing ground does Bessy have?
b. The farmer moves Bessy to another field and ties her to a post with the same rope at the corner of a closed shed 3 m by 3 m in the field. How many square meters of grazing ground does Bessy have? Explain your method for finding the area.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems80. You have a coupon worth $18 off the purchase of a scientific calculator. At the same time the calculator is offered with a discount of 15%, but no further discounts may be applied. For what tag price on the calculator do you pay the same amount for each discount?81. Without solving them, say whether these equations will have a positive solution, a negative solution, a zero solution, or no solution. Explain your choice.
a. 3 x=5
b. 5 z+7=3
c. 7−5w=3
d. 4 a=9a
e. y= y+1
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Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems83. What prism would this net form? Name, draw and label the 3-dimensional figure. (Not drawn to scale)
84. Given the following nets, find the areas of each of the polygons. Then find the total area of the net.a. b.
c. d.
Need Help? Check out these related resources. Learnzillion: Identify the Parts of Three-Dimensional Solids
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems Learnzillion: Analyze rectangular prisms to find surface area.
http://learnzillion.com/lessons/1220-analyze-rectangular-prisms-to-find-surface-area-part-1 Learnzillion: Represent Three-Dimensional Figures with Nets
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85. Find the surface area of the following prisms.
86. You need to replace the canvas of your tent. Canvas covers all sides, front, back, and the bottom. Your tent resembles the one in the picture to the right (the other sides of the front triangle are about 4.7 feet long). If the canvas costs $1.40 per square foot, how much will it cost to replace the canvas on your tent?
87. The following rectangular prisms have the same surface area. Find the height of the second rectangular prism.
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
88. The surface area of the triangular prism is 756 cm2. Find the length of the slant of the triangular prism.Edgar set up his equation as follows:
S=2∙ area of side triangles+ perimeter of triangle ∙ height of prism
756=2( 12∙12 ∙9)+ (12+9+x )9
Explain to Edgar where he made a mistake setting up the situation. Help him understand his misconception.Set up the situation correctly, and find the length of the slant of the triangular prism.
89. Yad Vashem Holocaust Museum in Israel. Most of the Museum's concrete and glass "main body" is hidden within the Mount of Remembrance, on which the Yad Vashem campus is situated, allowing little more than its 500 feet elongated, angular spine to convey a sense of its true scale.At one end of the spine, closest to the Museum's entrance and to the Visitors Center, a large triangular prism cantilevers outward over the valley floor, seemingly floating into space. The other end is open and glass from floor to ceiling bursting to a view of modern day Jerusalem.The front of the triangle has the following dimensions:
If all of the surfaces are made of concrete (except for the end made of glass), how many square feet of concrete were needed to build this part of the museum?Visit:
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
90.
Use the information on this advertisement to determine:a) The amount of material used to make the tent.b) The amount of floor space per person.91. This A-frame chalet needs to have the roof shingled. Determine the surface area of the roof given the following dimensions:
Height of the chalet = 7.1 mHeight of the prism = 6 mSlant height of the chalet = 7.5 mLength across the front of the chalet = 5 mWhich dimension(s) were not necessary? Explain your reasoning.
92. Review: Simplify each of the following expressions.
94. A box of aluminum foil and a box of tissues are rectangular prisms, as shown below. They have the same volumes. What is the height (h) of the tissue box?
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
95. Calculate the volume and the surface area of the prism at right. Show your work.
96. Calculate the volume of the prism below. Explain the strategy that you used.
97. Calculate the volume. Do you have enough information given to calculate the surface area? If yes, calculate the surface area. If not what else is needed?
98. Calculate the volume.
99. To properly fill the aquarium at left, the water level should be 1.5 inches from the top of the aquarium. If the
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problemsaquarium is filled properly, how many cubic inches of water will it contain?
100. The figure below shows the dimensions of foam used to package a product. The foam is in the shape of a rectangular prism with a smaller rectangular prism removed.
How many cubic centimeters of foam are used to package this product?101. A bank teller fills 3 drawers with stacks of $20 bills. The dimensions of each stack are approximately 3 cm x 6 cm x 15 cm. The dimensions of one drawer are 12 cm x 30 cm x 60 cm.
How many stacks will fill 3 drawers?
102. A window box shaped like a rectangular prism has a length of 12 feet, a width of 9 inches, and a height of 9 inches. If one bag of soil contains 2 cubic feet of soil, how many bags of soil are needed to fill the window box?
Module 2B: Problem Solving with Expressions, Equations, & Inequalities Accelerated 7th Grade Mathematics Additional Problems
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TenMarks: Volume of a Triangular Prismhttps://www.youtube.com/watch?v=qw7NAquWuTs
