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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?

Respuesta :

Answer:9 hr in a week

Step-by-step explanation:

Given

katya makes $20 per hour in tutoring and $8.50 per hour working in bookstore

Let us assume katya works for x hours in tutoring  and y hr  in bookstore

therefore the money made by katya is

total money=20x+8.5y

(b)Tution for one semester is $5736 (16 weeks)

Katya works 21 hours each week in book store

therefore in 16 weeks katya earns =16\times 21\times 8.5=$ 2856

Thus remaining amount can be earned 5736-2856=2880

therefore katya needs to work [tex]\frac{2880}{20}=144 hr [/tex]

144 hours in 16 weeks

for 1 week katya needs to work 9 hr.
  • Let's represent:

Number of hours spent tutoring = t

Number of hours spent working in a bookstore = b

  • Amount Katya earns tutoring = $20
  • Amount Katya earns at the bookstore = $8.50

The algebraic equation to represent the total amount of money Katya earns tutoring and working in the bookstore is written as:

$20 x t + $8.50 x b

20t + 8.5b

The tuition for one semester (16 weeks) is $5,736.

The tuition per week is calculated as:

$5,736/16

= $358.50

  • If Katya works 21 hours each week in the bookstore, the next step would be to calculate how many hours she must work tutoring to earn 358.50

Number of hours she must work per week as a tutor =

20t + 8.5b = 358.50

Number of hours spent working in a bookstore per week = b = 21 hours

  • We substitute 21 hours for b in the algebraic equation

20t + 8.5 x 21 = 358.50

20t + 178.50 = 358.50

  • Subtract 178.50 from both sides

20t + 178.50 - 178.50 = 358.50 - 178.50

20t = 180

  • Divide both sides by 20

20t/20 = 180/20

t = 9 hours

The number of hours she must work tutoring per week is 9 hours.

  • The total number of hours she must work per week to pay her tuition is calculated as:

Number of hours working in the bookstore per week + Number of hours working in the tutoring

21 hours + 9 hours

= 30 hours

Therefore, the total number of hours she must work per week to pay her tuition is 30 hours.

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