Linear Equation Word Problems

Question

A barber offers two options at his barbershop: a $15.00 regular haircut and a $20.00 deluxe haircut. On a certain day, the barber gave r regular haircuts and 3 fewer deluxe haircuts than regular haircuts. He earned $500.00 total from the two types of haircuts. Which of the following equations best models this situation?

Answer Choices:

A. 15.00r+20.00(r−3)=500.00

B. 15.00r+20.00(r+3)=500.00

C. 15.00(r−3)+20.00r=500.00

D. 15.00(r+3)+20.00r=500.00

Answer 1

$15 for a regular haircut

$20 for a deluxe haircut

3 less deluxe than regular cuts

d = r-3

d+r = 500

20d +15r = 500

20(r-3) + 15r = 500

20r -60 +15r = 500

35r = 560

r = 560/35 = 80/5 = 16 regular cuts

d = r-3 = 16-3 = 13 deluxe cuts

answer A is correct 15.00r + 20.00(r-3) = 500.00

15(16) + 20(13) = 500

20(13) + 15(16) = 260 + 240 = 500