Literal EquationsA Literal Equation is an equation that contains two or more variables.You are ordering pizza and sandwiches. You have

a budget of $80. How many sandwiches can you buy if you buy 4 pizzas? 7 pizzas?

MENU

Pizza

$10

Sandwich

$5This situation can be modeled using a Literal Equation.

10 5 80p s

cost per

pizza

# of pizzas

cost per sandwic

h

# of sandwiches

10 5 80p s 10 10p p 5 80 10s p 5 5 5

6 21s p 4 pizzas

6 21s p

2(16 )s 48s

7 pizzas

6 21s p

2(16 )s 72s

That was easy

More Literal EquationsSolve each equation for y. Then find the value of y for each value of x.

2 5y x 1, 0, 3x

2 2x x 2 5y x

( )2 5y 17y

( )2 5y 05y

( )2 5y 31y

2 5y x 1, 2, 3x

5 4 4x y

5 4 4x y 4 4y y 5 4 4x y 5 5x x

4 5 4y x 4 4

5 44

yx

I don’t like fractions.

(5 44)

y 1

1

0.254

y

(5 44)

y 2

31.5

2y

(5 44)

y 3

11

2.754

y

Literal Equationswith Only Variables

Solve each equation for x.

A B Cxt C C A xC B t Bt Bt

A Cx

Bt

ba

cx

ac xb b b

x ac b

mx n px Use the distributive property in reverse.

( )m xn nx mx So that means...

( )x x xm n m n

mx n px ( )x m n p

m n m n

px

m n

Asi de

Facil

FormulasPerimeter of a Rectangle 2 2P l w

Circumference of a Circle 2C r

Area of a Rectangle A lw

Area of a Triangle12

A bh

Area of a Circle 2A r

Distance Traveled d rt

Temperature (Celsius) 3 )59

( 2FC

Working with FormulasWhat is the radius of a circle with circumference 64 feet? Round to the nearest tenth.

2C r

2 2

2r

C

)2(

r

64

10.2r

A car travels on a highway at a rate of 65 mph. How long does it take for the car to travel 25 miles? Round to the nearest tenth.

d tr r r

tdr

2565

t

.4t hours

That was easy

Homework

Page 112 - 113: 12 – 34Even Numbers Only

Comparison of Regular Equations & Literal

Equations

5 4 4x 4 4

5 4 4x 4 4 5 4

4x

5 4

4x

5 4 4y x 4 4 5 4 4y x

4 4

Solve for x.

5 44

yx

5 4

4y

x

Solve for r.

13 2 r 2 2

132

r

2C r 2 2

2C

r

Asi de Facil

Rewriting a FormulaThe following formula is used to convert degrees Fahrenheit to degrees Celsius.

3 )59

( 2FC

Rewrite the formula to convert degrees Celsius to degrees Fahrenheit.

3 )59

( 2FC 5 5

9 9

932

5C F

32 32

932

5F C

The following formula is used to calculate the Surface Area of a cylinder.

22 2rhA r

Rewrite the formula to solve for h.

22 2hA r r2 22 2r r

22 2A r rh

2 2r r

222

A rh

r

More Rewriting FormulasSolve each equation for the given variable.

2z

y ax

xf or

2 2

2x zy a

1 1y y

21y z

ax

2yz

x ya

3f or

bay bA

y y

3A ay

b

( ) 3by a A

3ay by A ay ay

3by A ay

y y3A ay

by

3 5( ) f or bxba

3 3 5a b x 3 3a a 3 5 3b x a 3 3

5 33

x ab

That was easy

Homework

Page 113: 36 - 41

Page 112: 12, 14, 16

Solve each equation for y. Then find the value of y for each value of x.

2, 1, 3x 2 4 8y x

2 4 8y x 4 4x x

2 4 8y x 2 2

2 4y x

2 4( )y 28y

2 4( )y 12y

2 4( )y 3 2y

4, 5, 6x

4 3 7x y

4 3 7x y 7 7

4 7 3x y3 3

4 73

yx

43

( ) 7y

47.6

43

( ) 7y

5 9

43

( ) 7y

610.3

2, 1, 0x 6 7 4x y

6 7 4x y 7 7

6 7 4x y 4 4

6 74

yx

(4)6 7

y 2

4.75

(4)6 7

y 1

3.25

(4)6 7

y0 1.75

Page 112: 20, 22, 24, 26

Solve each equation for x.

ax x c

( )1x a c

1 1a a

1c

xa

yx vb

by x v v v

x by v

x ya bxb ay

b b

ay

xb

4( )x b x

4 4x b x 4 4b b 4 4x x b

x x

3 4x b 3 3

43b

xThat was easy

Hey, that has an x on both sides!

Page 112 - 113: 28, 30, 34

Solve each equation for the appropriate variable.

What is the radius of a circle with circumference 22 m? 2C r

2 2

2r

C

)2(

r

22

3.5r

A triangle has height 4 ft and area 32 ft2. What is the length of its base?

12

A hb 1 1

2 2

2A hb h h

2b

Ah

( )2( )

b 324

16b

You can use the following formula to find the batting average, A, of a batter who has h hits in n times at bat. If a batter has a batting average of .290 and has been at bat 300 times, how many hits does he have?

Anh

h An

( )( )h .290 300

87h Asi de

Facil

Homework

Page 112 - 113: 11 - 35Odd Numbers Only