Question

Sebastian is working to summer jobs, making $8 per hour walking dogs and $10 per hour clearing tables. In a given week, he can work no more than 12 total hours and must earn a minimum of $100. If X represents the number of hours walking dogs and Y represents the number of hours clearing tables, right and solve a system of inequalities graphically and determine one possible solution.

Answer 1

The graph in the attached figure

One possible solution is the ordered pair (3,8)

see the explanation

Explanation:

Let

x ---> the number of hours walking dogs

y ----> the number of hours clearing tables

we know that

He can work no more than 12 total hours

so

`x+y\leq 12` ----> inequality A

He must earn a minimum of $100

so

`8x+10y\geq 100` ----> inequality B

Solve the system of inequalities by graphing

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie in the shaded area of the solution set (the ordered pair makes true both inequalities)

so

One possible solution is the ordered pair (3,8)

That means

In the given week, the number of hours walking dogs was 3 and the number of hours clearing tables was 8

Verify algebraically

Substitute the value of x and the value of y in the inequality A and in the Inequality B

inequality A

`3+8\leq 12`

`11\leq 12` ----> is true

Inequality B

`8(3)+10(8)\geq 100`

`104\geq 100` ---> is true

therefore

the ordered pair (3,8) is a possible solution of the system