Question

Katya tutors and works in the college bookstore to pay for her college tuition. She makes $20 per hour tutoring and $8.50 per hour working in the bookstore. a) Write an equation to represent the total amount of money Katya earns tutoring and working in the bookstore. b) The tuition for one semester (16 weeks) is $5,736. If Katya works 21 hours each week in the bookstore, how many hours per week must she tutor to pay her tuition?

Answer 1

We have to write the equation which represents Katya's earnings while tutoring and working in a book store is given as follows:  

She makes $20 an hour while tutoring. Let's say she tutors for 'x' hours in a day. So, she will make $20 \times x = 20x$ dollars by tutoring in a day.

She makes $8.50 an hour while working in the bookstore. Let's say she works for 'y' hours in the bookstore in a day. She will make $8.50 \times y = 8.50y$ dollars by working in the bookstore.

Therefore, the equation representing her total amount of money that she makes from both the places is given by:

$(20x + 8.50 y)

Since, Tution for 16 weeks is $5,736.  So the amount of tuition for each week is =$\frac{5736}{16}$= 378.5 dollars

So, Katya needs to make 378.50 dollars a week.

Since, She worked for 21 hours in the book store, so she makes  

$21 \times 8.50$ dollars= 178.50 dollars a week from the bookstore

So, now she needs to make = 378.50 - 178.50 = $180 a week while tutoring

Since she makes 20 dollars an hour from tutoring.  

She needs to tutor =$\frac{180}{20}$ =9 hours a week to make the rest of the tuition.

So, Katya has to work for 9 hours in tutoring.