Question

Riley is working two summer jobs, making $7 per hour walking dogs and making $25 per hour tutoring. In a given week, she can work no more than 18 total hours and must earn no less than $270. If Riley worked 4 hours walking dogs, determine the maximum number of whole hours tutoring that she can work and still meet her requirements. If there are no possible solutions, submit an empty answer.

Answer 1

Answer:

Riley can work for 10 hours for tutoring and can meet the requirement.

Step-by-step explanation:

Let the number of hours of walking dogs be 'x'.

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

Given:

Number of hours she can work $\leq$ 18

Now number of hours of work is equal to sum of the number of hours of walking dogs and the number of hours of tutoring.

framing in equation form we get;

$x+y\leq 18$

Also Given:

Cost per hour for walking dogs = $7

Cost per hour for tutoring = $25

Total Money she must earn $\geq$ 270

Now Cost per hour for walking dogs multiplied by the number of hours of walking dogs plus Cost per hour for tutoring multiplied by Cost per hour for tutoring.

framing in equation form we get;

$7x+25y \geq 270$

Now Given:

Number of hours worked for walking dogs = 4

We need to find maximum number hours tutoring that she can work.

Substituting the value of x as we get;

$7\times4+25y\geq 270\\\\28+25y\geq 270$

Subtracting both side by 28 we get;

$28+25y-28\geq 270-28\\\\25y\geq 242$

Dividing both side by 25 we get;

$\frac{25y}{25} \geq \frac{242}{25} \\\\y \geq 9.68$

Hence If we consider y =10 and x =4 the requirement to earn $270 will be fulfilled and also maximum number of hours of work of 18 is also fulfilled.

Hence Riley can work for 10 hours for tutoring and can meet the requirement.

Answer 2

Answer:

14

Step-by-step explanation:

The values of t that make BOTH inequalies true are:

{10, 11, 12, 13, 14}

Therefore the maximum number of hours tutoring that Riley must work is 14.