Alice spent $131 on shoes. Flip flops cost $15 and Sneakers cost $28. If she bought a total of 7 shoes, then how many of each kind of shoe did she
buy? Write the answer as an ordered pair...(flip flops, sneakers). Do not
include the units. *

Flip flops = 5

Sneakers = 2

Step-by-step explanation:

Let

x = flip flops

y = sneakers

x + y = 7 (1)

15x + 28y = 131 (2)

From (1)

x = 7 -y

Substitute x = 7 - y into (2)

15x + 28y = 131

15(7 - y) + 28y = 131

105 - 15y + 28y = 131

-15y + 28y = 131 - 105

13y = 26

y = 26/13

= 2

y = 2

Substitute y = 2 into (1)

x + y = 7

x + 2 = 7

x = 7 - 2

= 5

x = 5

Flip flops = 5

Sneakers = 2

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .