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 then 19 total hours and must earn at least $170. If Jacob worked 4 hours landscaping, determine the minimum number of whole hours washing cars he must work to meet his requirements.

Answer 1

Answer:

Jacob should work minimum of 14 hours washings cars to meet his requirement.

Step-by-step explanation:

Let the number of hours of washing cars be 'x'.

Let the number of hours of landscaping be 'y'.

Given:

Cost for Per hour for washing cars = $10

Cost for per hour Landscaping = $8

Total number of hours of working $\leq 19$

Amount to be earned this weekend $\geq \ 170$

So we can say that;

$x+y\leq 19$

Also,

Amount to be earned this weekend should be greater than or equal to sum of Cost for Per hour for washing cars multiplied by number of hours of washing cars and Cost for per hour Landscaping multiplied by number of hours of landscaping.

framing in equation form we get;

$10x+8y\geq 170$

Now Number of hours he worked for landscaping $y=4$

So we get;

$10x+8\times4\geq 170\\\\10x+32\geq 170$

Subtracting both side by 32 we get;

$10x+32-32\geq 170-32\\\\10x\geq 138$

Dividing both side by 10.

$\frac{10x}{10}\geq \frac{138}{10}\\\\x\geq 13.8$

Hence Jacob should work minimum of 14 hours washings cars to meet his requirement.