Question

Your time spent playing pool and ice skating must not exceed 20 hours a week. Your weekly allowance is $80. You pay $3 an hour playing pool and $5 an hour for ice skating. Write the inequalities that represent the situation. Identify two possible solutions to this situation.

Answer 1

The graph in the attached figure

Two possible solutions are the point (10,10) and the point (4,8)

see the explanation

Explanation:

Let

x ----> the time in hours spent playing pool in a week

y ----> the time in hours spent for ice skating in a week

we know that

`x+y \leq 20` ----> inequality A

`3x+5y \leq 80` -----> inequality B

using a graphing tool

The solution is the shaded area

see the attached figure

Remember that the time can not be a negative number

If a ordered pair is a solution of the system of inequalities, then the ordered par must lie on the shaded area of the solution

Looking at the graph

Two possible solutions are

(10,10) ----> this point lie on the shaded area of solution

That means -----> The time in hours spent playing pool in a week is 10 and the time in hours spent for ice skating in a week is 10

(4,8) ----> this point lie on the shaded area of solution

That means -----> The time in hours spent playing pool in a week is 4 and the time in hours spent for ice skating in a week is 8