Question

Autumn is working two summer jobs making $16 per hour tutoring and making $12 per hour landscaping.In a giving week she can work...

Answer 1

Answer:

{13,14}

Step-by-step explanation:

Let

x ----> number of hours per week of tutoring

y ----> number of hours per week of landscaping

we know that

She can work no more than 17 hours

so

$x+y\leq 17$ -----> inequality A

She must earn at lest $240

The term " at least" means, "greater than or equal to"

$16x+12y\geq 240$ ----> inequality B

If Autumn worked 3 hours landscaping

then

$y=3\ hours$

substitute in the inequality A and in the inequality B

Inequality A

$x+3\leq 17\\x \leq 17-3\\x\leq 14\ hours$

Inequality B

$16x+12(3)\geq 240\\16x\geq 240-36\\x\geq 12.75\ hours$

The solution of the system is the interval {12.75,14]

All possible values for the number of whole hours tutoring that she must work to meet her requirements are

{13,14}