Literal Equations A 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 $ 5 This situation can be modeled using a Literal Equation. 10 5 80 p s cost per pizza # of pizzas cost per sandwic h # of sandwiche s 10 5 80 p s 10 10 p p 5 80 10 s p 5 5 5 6 2 1 s p 4 pizzas 6 2 1 s p 2 ( 16 ) s 4 8 s 7 pizzas 6 2 1 s p 2 ( 16 ) s 7 2 s That was easy
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Literal Equations A Literal Equation is an equation that contains two or more variables. You are ordering pizza and sandwiches. You have a budget of $80.
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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?