Question

Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. In a given week, he can work no more than 19 total hours and must earn at least $170. If Jacob worked 4 hours landscaping, determine the minimum number of whole hours washing cars that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.

Answer 1

Answer:

Step-by-step explanation:

Let x represent the number of hours that that he spent washing cars.

Let y represent the number of hours that that he spent landscaping.

In a week, he can work no more than 19 total hours. This means that

x + y ≤ 19- - - - - - - - - - - -1

Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. He must earn at least $170. This means that

10x + 8y ≥ 170 - - - - - - - - - -2

If Jacob worked 4 hours landscaping, it means that

x + 4 ≤ 19

x ≤ 19 - 4

x ≤ 15

Also,

10x + 8 × 4 ≥ 170

10x + 32 ≥ 170

10x ≥ 170 - 32

10x ≥ 138

10x ≥ 138/10

x ≥ 13.8

The minimum number of hours is 14

Answer 2

Answer:

Let x represent the number of hours that that he spent washing cars.

Let y represent the number of hours that that he spent landscaping.

In a week, he can work no more than 19 total hours. This means that

x + y ≤ 19- - - - - - - - - - - -1

Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. He must earn at least $170. This means that

10x + 8y ≥ 170 - - - - - - - - - -2

If Jacob worked 4 hours landscaping, it means that

x + 4 ≤ 19    x ≤ 19 - 4    x ≤ 15

Also,  10x + 8 × 4 ≥ 170     10x + 32 ≥ 170

10x ≥ 170 - 32          10x ≥ 138

10x ≥ 138/10             x ≥ 13.8

The minimum number of hours is 14