Question

Mandy spent $287 on 7 pairs of shoes. She purchased some pairs of boots that cost $65 per pair and some pairs of workout shoes that cost $23 per pair.

Answer 1

• b=3

,

• w=4.

Step-by-step explanation:

A pair of boots (b) costs $65 per pair.

A pair of workout shoe (w) costs $23 per pair.

Mandy bought 7 pairs of shoes, therefore:

`b+w=7`

She spent $287:

`65b+23w=287`

Next, solve the system of equations for b and w:

`\begin{gathered} b+w=7 \\ 65b+23w=287 \end{gathered}`

From the first equation, b=7-w

Substitute into the second equation:

`\begin{gathered} 65b+23w=287 \\ 65(7-w)+23w=287 \\ 455-65w+23w=287 \\ -42w=287-455 \\ -42w=-168 \\ w=(-168)/(-42) \\ w=4 \end{gathered}`

Finally, solve for b:

`\begin{gathered} b=7-w \\ b=7-4 \\ b=3 \end{gathered}`

The solution to the system is: b=3, w=4.