Question

A local car wash charges $8 per wash (w) and $10 for a wash and wax (x). At the end of a certain day the total sales were no more than $1300 and there were no more than 350 of either service provided. Write down a system of inequalities to model this situation.

Answer 1

See below in bold.

Explanation:

Consider the costs, we have:

8w + 10x ≤ 1300.

The services:

w + x ≤ 350.

Answer 2

`w+x\leq 350`

`8w+10x \leq 1300`

Explanation:

Let's call
`w` each wash and
`x` the wax.

We know by given that the car wash charges $8 per wash and $10 per wax, this can be expressed as

`8w` and
`10x`

A certain day, the total sales were no more than $1300 and there were no more than 350 of either service.

This information can lead to the following system of inequalities

`w+x\leq 350`

`8w+10x \leq 1300`

The image attached shows the solution to this sytem.

Remember that the solution is always the intersection between both shaded regions, in the image is marked with S.

Therefore, the answer to the question is

`w+x\leq 350`

`8w+10x \leq 1300`