you have 2 part time jobs

Question

You earn $6 per hour running errands and  $5 per hour walking dogs. You can work a total of 10 hours this weekend and hope to earn at least $55. Let r be the number of hours you spend running errands.

A. Write an inequality that discribes the situation. Your inequality should involve only one variable, r.

B. If you spend the same amount of time at each job, will you meet your goal? Explain.

C. Can you meet your goal working all 10 hours at only one job? Explain.

Answer 1

Let r = the number of hours spent running errands

Let q = the number of hours spent walking dogs

 

 

A)

 

Since you can only work a total of 10 hours, we can write the equation

 

r + q = 10   

 

 

Since you hope to earn at least $55, we write the inequality

 

6r + 5q ≥ 55

 

 

We want the inequality in terms of r.  So we can substitute the equation into the inequality.

 

 

6r + 5(10 - r) ≥ 55

6r + 50 - 5r ≥ 55

 

r + 50 ≥ 55

 

 

B)

 

If you spent the same amount of time at each job, then the maximum number of hours you work for each job is 5.  This is because 5+5=10, the total amount of hours you can work.

 

Plug in 5 into the inequality.  r = 5 = q

 

5 + 50 ≥ 55

 

55 ≥ 55

 

 

This statement is true.  Therefore, you will meet your goal.

 

 

C)

 

We evaluate the amount of money you earn running errands for $6 per hour, and we evaluate  the amount of money you earn walking dogs for $5 per hour.

 

r = 10 = q

 

 

Running errands:

 

6(10) = 60

 

You earn $60 at this job.  This is more than $55.

 

 

 

Walking dogs:

 

5(10) = 50

 

You earn $50 at this job.  This less than $55.

 

 

In conclusion, if you only run errands, then you will meet your goal.