Answer:
One possible solution is Jace spends 5 hours lifeguarding and 8 hours washing cars
Step-by-step explanation:
The parameters of the two summer jobs Jace is working are;
The amount Jace makes for Lifeguarding = $18 per hour
The amount Jace makes for washing cars = $10 per hour
The number of hours he can work a week ≤ 13 hours
The amount he must earn in a ≥ $170
Whereby we have;
x = The number of hours Jace spends lifeguarding
y = The number of hours Jace spends washing cars
The system of inequalities are;
x × 18 + y × 10 ≥ 170
x + y ≤ 13
Making y the subject of the formula of both inequalities gives;
For the first inequality, we have;
x × 18 + y × 10 ≥ 170
10·y ≥ 170 - 18·x
y ≥ 170/10 - 18/10·x
y ≥ 17 - 1.8·x
For the second inequality, we have;
x + y ≤ 13
y ≤ 13 - x
Graphing both inequalities is drawn using Microsoft Excel
Equating both inequalities, given in relation to the y-values, the point where the two lines representing both inequalities meet is given as follows;
17 - 1.8·x = 13 - x
17 - 13 = 1.8·x - x
4 = 0.8·x
x = 4/0.8 = 5
y ≤ 13 - x gives;
y ≤ 13 - 5
y ≤ 8
Given that both relationships are either ≤ or ≥, we have the point where both inequalities meet is one possible solution
Therefore;
One possible solution is x = 5 hours, y = 8 hours
The number of hours Jace spends lifeguarding = x = 5 hours
The number of hours Jace spends washing cars = y = 8 hours.
