Math Word Problem

Question

A waitress sold 17 ribeye steak dinners and 30 grilled salmon dinners, totaling $580.08 on a particular day. Another day she sold 24 ribeye steak dinners and 15 grilled salmon dinners, totaling $ 581.87. How much did each type of dinner cost?

Answer 1

Hello Freddy,

you would set up 2 equations describing sales for each day:

if R = ribeye cost and S = grilled salmon cost:

A waitress sold 17 ribeye steak dinners and 30 grilled salmon dinners, totaling $580.08 on a particular day:

17R + 30S = 580.08 ----> #1

Another day she sold 24 ribeye steak dinners and 15 grilled salmon dinners, totaling $ 581.87:

24R + 15S = 581.87 -------> #2

Multiply equation #2 by -2; that way you can eliminate S when you add both equations:

#1: 17R + 30S = 580.08

#2 times (-2): -48R - 30S = -1163.74

Add both equations: -31R = -583.66

Divide both sides by -31: R = 18.8277 which you can round up to 18.83 since we usually only keep 2 decimal digits for money.

Plug that answer in equation #1: 17(18.83) + 30S = 580.08 ---> 320.11 + 30 S = 580.08 ---> 30S = 259.97

Divide both sides by 30 ---> S = 8.66566 which you can round up to 8.67

so a ribeye dinner cost $18.83 and a salmon dinner cost $8.67

Cheers.