Question

Mila is working two summer jobs, making $13 per hour landscaping and making $10 per hour clearing tables. In a given week, she can work a maximum of 13 total hours and must earn a minimum of $140. If x represents the number of hours landscaping and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

x≤3.33, y≤9.67

Explanation:

Number of hours landscaping =x

Number of hours clearing tables= y

If she can work a maximum of 13 total hours. Then:

x+y≤13

Mila makes $13 per hour landscaping and making $10 per hour clearing tables.

Income: 13x+10y

She must earn a minimum of $140.

Therefore:

13x+10y≥140

We then solve the two resulting simultaneous inequalities.

x+y≤13

13x+10y≥140

From the graph, at the point of intersection of the two inequalities. One possible solution is:

x≤3.33, y≤9.67

Therefore, to meet her minimum target, she can work 3.33 hours landscaping and 9.67 hours clearing tables.

Check:

From the first inequality: x≤13-y

Substitute into 13x+10y≥140

13(13-y)+10y≥140

169-13y+10y≥140

-3y≥140-169

-3y≥-29

Divide both sides by -3

y≤9.67

Recall:

x≤13-y

x≤13-9.67

x≤3.33