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CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
DO MORE! – Solving Literal Equations & Re-‐arranging Formulas
Directions: Solve the equation below. Directions: Graph the equation below.
1. 6r8 = 2(r + 2)
16
2. y = 𝟏𝟐𝒙 − 𝟐
Directions: Solve the task below. Read the scenarios carefully. In January of 2010 the national average for 5 gallons of gasoline was $15.
1. Create an equation that models the scenario above. Assume “x” represents a gallon of gasoline.
2. What was the national average for 1 gallon of gasoline in 2010?
3. What was the price for 10 gallons of gasoline in 2010?
Essential Question: How is solving a literal equation or formula for a specific variable similar to solving an equation? How is it different?
AIM: KWBAT ____________________ formulas and _____________________ to solve for a certain variable.
Standard: MCC9-‐12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
Cycle 1 – Solving Literal Equations and Formulas
• A _______________________________ is a type of equation that contains one or more variables.
• A _______________________________ is a literal equation that states specific rules or relations among quantities.
• Solving __________________________ literal equation is just like solving a regular equation. Our jobs to _______________________________, using inverse operations.
• Remember, when coefficient are fractions we multiply both sides by the coefficient’s reciprocal of the fraction.
Example 1 Example 2 Example 3
Perimeter = Twice the Length + twice the Width
Solve for the length, l:
𝑃 = 2𝑙 + 2𝑤
𝟑𝒛+ 𝒚 = 𝟓+ 𝟓𝒛; 𝑺𝒐𝒍𝒗𝒆 𝒇𝒐𝒓 𝒛. Below is the formula for converting degrees Fahrenheit to
Celsius
Solve for F:
Example 4 Example 5 Example 6
!!!!!
= 𝑎 ; Solve for b
2𝑥 + 2𝑦 = 10; Solve for x
12𝑥 − 4𝑦 = 20; Solve for y.
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
1. Area = Length x Width 𝐴 = 𝑙 ∙ 𝑤 ; Solve for w:
2. Solve 8𝑐 = 4𝑑 + 12 for c:
3. x = 5y for y
4. s + 4t = r for s
5. 3m − 7n = p for m 6. 6 = hj + k for j
7. 4c = d for c
8. n − 6m = 8 for n 9. 2p + 5r = q for p
10. −10 = xy + z for x
11. 5yr = 8 for r 12. 𝒗𝟓= 𝟒𝒕
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
Scholar Bingo Directions: Silently and independently complete each row, in order of B.I.N.G and O. Once you finish a row, walk to the key and check your answers. First to get “BINGO!” gets 2 merit points and a prize.
B I N G O!!! 1. Solve for c:
𝐴 = 𝐵 + 𝐶
6. Solve for v: 3𝑑 = 7𝑣 + 5
11. Solve for w:
𝑃 =4𝑤ℎ!
16. Solve for y: 𝑎𝑥 + 𝑏𝑦 = 𝑐
21. Solve for y: −20𝑥 − 5𝑦 = 30
2. Solve for x: 𝑥 − 𝑏 = 𝑎
7. Solve for h: 7𝑎 = 10 − 2ℎ
12. Solve for w: 𝑃 = 2𝑙 + 2𝑤
17. Solve for y: 6𝑥 − 3𝑦 = 15
22. Solve for y: 6𝑥 + 12𝑦 = −18
3. Solve for k: −3𝑘 = 𝑚
8. Solve for p: 20𝑥 + 5𝑝 = 𝑤
13. Solve for z: 3𝑧 + 𝑦 = 5 + 5𝑧
18. Solve for y: 5𝑥 + 10𝑦 = −20
23. Solve for c:
𝑎 =𝑎 + 𝑏 + 𝑐
3
4. Solve for g: 𝑎𝑒𝑔 = 10
9. Solve for k: 4𝑎𝑏 + 𝑘 = 13
14. Solve for d: 8𝑐 = 4𝑑 + 12
19. Solve for y: −9𝑥 − 3𝑦 = 6
24. Solve for E:
𝑚 =2𝐸𝑉!
5. Solve for y:
𝑦3= ℎ
10. Solve for a: 7𝑎 − 8𝑏 = 10𝑥
15. Solve for y: 𝑎(𝑦 + 1) = 𝑏
20. Solve for y: −15𝑥 + 5𝑦 = 25
25. Solve for C:
𝐹 =95𝐶 + 32
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
Cycle 2 – Interpreting & Solving Literal Equations in Word Problems
Example 1 In physics there’s a very useful formula:
distance = rate x time. Or d = rt
Kenyarda is driving her old VW Bug car to college, the University of Virginia and she wants to get there in 3 hours to meet her roommate. If her college is 200 miles away from home, how fast will she have to drive?
Example 2 When working with a rectangle, we know the formula for its perimeter is:
Perimeter = Twice the Length + Twice the Width or P = 2l + 2w
You and your college roommate decide to build a small rectangular pool in the backyard. The pool’s length is four less than triple its width. It’s width is 4 meters. Find the perimeter.
1. The formula K = C + 273 is used to convert temperatures from degrees Celsius to Kelvin. Solve this formula for C.
2. The formula d = rt relates the distance an object travels d, to its average rate of speed r, and amount of time t that it travels.
a. Solve the formula d = rt for t.
b. How many hours would it take for a car to travel 150 miles at an average rate of 50 miles per hour?
3. The formula F − E + V = 2 relates the number of faces F, edges E, and vertices V, in any convex
polyhedron.
a. Solve the formula F − E + V = 2 for F.
b. How many faces does a polyhedron with 20 vertices and 30 edges have?
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4
4. The formula C = 2πr relates the radius r of a circle to its circumference C. Solve the formula for r.
5. The formula y = mx + b is called the slope-‐intercept form of a line. Solve this formula for m.
6. The formula c = 5p + 215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending.
a. Solve the formula c = 5p + 215 for p
b. If Allie’s parents are willing to spend $300 for
a party, how many people can attend?
7. The formula for the area of a triangle is A = 12bh, where b represents the length of the base and h
represents the height.
a. Solve the formula A = 12bh for b.
b. If a triangle has an area of 192 mm2, and the height measures 12 mm, what is the measure of the base? 8. The formula N = 7LH is used to determine N, the number of bricks needed to build a wall that is L
feet in length and H feet high. A customer would like a wall constructed that is 4 feet high. If the bricklayer wants to use all of the 1,820 bricks that he has readily available, how long will the wall be?
CCGPS Coordinate Algebra 2014-‐2015 Name: Period: Date: Lesson 1.5.1 – AIM: KWBAT re-‐arrange formulas and solve literal equations for a certain variable. U Unit 1 – Relationship Between Quantities. Standards: CED. 4