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 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 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 == 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
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 = =9 hours a week to make the rest of the tuition.
So, Katya has to work for 9 hours in tutoring.