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Section 3.5 Applications and Problem Solving
Section 3.5 Applications and Problem Solving
Topics Covered
• Translating Verbal Statements Into Equations.
•Applications of Linear Equations
Translation ReviewAddition a+b:• the sum of a and b• a plus b• a increased by b• the total of a and b• b added to a*• b more than a*
Subtraction: a – b:• the difference of a and b• a minus b• a decreased by b• b less than a*• b subtracted from a*
Multiplication (a)(b):• the product of a and b• a times b• a multiplied by b
Division a / b :• the quotient of a and b• a divided by b• b divided into a*• the ratio of a and b• a over b• a per b
* reverse order
Translating ExamplesThe sum of 12 and a number is 49. Find the number.
The difference of a number and 10 is 18. Find the number.
The quotient of a number and -2 is 10. Find the number.
A number subtracted from -30 results in 42. Find the number.
Eight more than twice a number is 20. Find the number.
Ten less than the quotient of a number and -6 is -2. Find the number.
Three times the difference of a number and 5 is 15. Find the number
The product of a number and -5 is -20. Find the number.
1. x+(-5) = -20 ; x = -15
2. -5x = -20 ; x = 43. -5x = -20 ; x = -154. x + (-5) = -20 ; x = -
25
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Negative four times a number when reduced by 6 equals 14. Find the number.
1. -4x – 6 = 14 ; x = -16
2. 6 – (-4x) = 14 ; x = 2
3. -4x – 6 = 14 ; x = -54. 6 – (-4x) = 14 ; x = -
2
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Four decreased by the product of a number and 7 is equal to 11. Find the number.
1. 4 – 7x = 11 ; x = -12. 4 – 7x = 11 ; x = 143. 7x – 4 = 11 ; x = 14. 7x – 4 = 11 ; x = 14
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Twice the sum of 9 and a number is 30. Find the number.
1. 2(9 + x) = 30; x = 32. 2(9) + x = 30; x =
123. 2(9) + x = 30; x = -
124. 2(9 + x) = 30; x = 6
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Negative five times the difference of 8 and a number is -55. Find the number.
1. -5(8) – x = -55; x = -15
2. -5(8 – x) = -55; x = -3
3. -5(8) – x = -55; x = -95
4. -5(x – 8) = -55; x = -19
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The difference of a number and 16 is the same as the product of the number and -3. Find the
number.
1. x – 16 = x – 3 ; x = 02. x – 16 = -3x; x = 83. x – 16 = x / 3 ; x =
244. x – 16 = -3x; x = 4
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Six less than a number is the same as 3 more than twice the number.
1. 6 – x = 2x + 3; x = 12. x – 6 = 2x + 3; x = -
93. x – 6 = 2x + 3; x = 94. 6 – x = 2x + 3; x = -
1
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Problem-Solving Process
Step1: Read the Problem carefully.
Step 2: Assign labels to unknown quantities.
Step 3: Write an equation in words
Step 4: Write a mathematical equation.
Step 5: Solve the equation.
Step 6: Interpret the result and write the final answer in words.
Application #1
Jackson scored three times as many points in a basket ball game as Tony did. If p represents the number of points that Tony scored, write an expression for the number of points that Jackson scored.
Application #2
At a concession stand, drinks cost $2 each. If Frank buys x drinks, write an expression for the total cost.
Application #3Carlita spent $88 less on tuition and fees than her friend Carlo did. If Carlo spent d dollars, write an expression for the amount that Carlita spent.
Race car driver A.J. Foyt won 15 more races than Mario Andretti. If Mario Andretti won r races, write an expression for the number of races won by A.J. Foyt.
1. 15r2. r -153. r + 154. r / 15
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Sandy bought eight tomatoes for c cents each. Write an expression for the total cost.
1. 8c2. c – 8 3. c + 84. c / 8
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Application #4
Richard and Linda enjoy visiting Hilton Head Island, South Carolina. The distance from their home to Hilton Head is 954 mi, so the drive takes them 2 days. Richard and Linda travel twice as far the first day as they do the second. How many miles do they travel each day.
Application #5
Two hikers on the Appalachian Trail hike from Hawk Mountain to Gooch Mountain. The next day, they hike from Gooch Mountain to Woods Hole. The total distance is 19 mi. If the distance between Gooch Mountain and Woods Hole is 5 mi more than the distance from Hawk Mountain to Gooch Mountain, find the distance they hiked each day.
Application #6
A two-piece set of luggage costs $150. If sold individually, the larger bag costs $40 more than the smaller bag. What are the individual costs for each bag?
Felicia has an 8-ft piece of ribbon. She wants to cut the ribbon into two pieces so that one piece is three times the length of the other. Find the length of each piece.
1. 3 ft and 9ft2. 3 ft and 5ft 3. 1 ft and 3 ft4. 2 ft and 6ft
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Becca paid a total of $695 for tuition and lab fees for fall semester. Tuition for her courses
cost $605 more than lab fees. How much did her tuition cost? What was the cost of the lab fees?
1. Tuition costs $1300 and lab fees cost $45
2. Tuition costs $650 and lab fees cost $45
3. Tuition costs $45 and lab fees cost $650
4. Tuition costs $635 and lab fees cost $60
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Mercedes is paid a salary of $480 a week at her job. She worked 8 hr of overtime during the holidays and her weekly paycheck came to $672. What is her overtime pay per hour?
1. $192 per hr2. $84 per hr3. $24 per hr4. $8 per hr
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The Beatles had 9 more number one albums than Elvis Presley. Together, they
had a total of 29 number one albums. How many number one albums did each have?
1. Beatles 20 , Elvis 92. Beatles 38 , Elvis 293. Beatles 20 , Elvis 114. Beatles 19 , Elvis 10
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