CED.4 Literal Equations & Re-Arranging Formulas

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.


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.


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


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


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?


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?


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CED.4 Literal Equations & Re-Arranging Formulas