Question

You can work at most 20 hours next week. You need to earn at least $90 to cover your weekly expenses. Your dog walking job pays $9.00 per hour and your job as a car wash attendant pays $10.00 per hour. This situation can be represented by a system of inequalities, where x = dog walking hours and y = car washing hours. Identify two possible combinations of hours you can work at both jobs. Create a system of linear inequalities and solve.

Answer 1

The answer in the procedure

Explanation:

Let

x ----> the dog walking hours

y ----> the car washing hours

we know that

The system of linear inequalities is equal to

`x+y\leq20` -----> inequality A

`9x+10y\geq 90` -----> inequality B

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

Two possible combinations of hours are

(10,10) and (0,9)

Verify

For (10,10)

Substitute the value of x and the value of y in both inequalities

Inequality A

`10+10\leq20`

`20\leq20` -----> is true

Inequality B

`9(10)+10(10)\geq 90`

`190\geq 90` ----> is true

therefore

(10,10) is a possible solution

For (0.9)

Substitute the value of x and the value of y in both inequalities

Inequality A

`0+9\leq20`

`9\leq20` -----> is true

Inequality B

`9(0)+10(9)\geq 90`

`90\geq 90` ----> is true

therefore

(0,9) is a possible solution