word problem

Question

A waitress sold 13 ribeye steak dinners and 18 grilled salmon dinners, totaling $550.25 on a particular day. Another day she sold 22 ribeye steak dinners and 6 grilled salmon dinners, totaling $582.08. How much did each type of dinner.

Answer 1

This is a systems of equations question.  Let's set ribeye steak to the variable r, and grilled salmon to s.

 

We get these two equations:

13r + 18s = 550.25

22r + 6s = 582.08

 

First, we'll isolate one variable in the first equation.  Let's choose r:

13r = 550.25 - 18s

r = 42.33 - 1.38s

 

Now, we'll take this value for r and plug it into the second equation:

22r + 6s = 582.08

22 (42.33 - 1.38s) + 6s = 582.08

(931.19 - 30.46s) + 6s = 582.08          | multiply values by 22

931.19 - 24.46s = 582.08                   | combine s values

349.11 = 24.46s                               | move 582.08 to left side, and combine;  move -24.46s to right side

14.27 = s                                        | solve for s

 

Now, plug this value for s back into the first equation:

13r + 18s = 550.25

13r + 18 (14.27) = 550.25

13r = 256.91 = 550.25

13r = 293.34

r = 22.56

 

So r = 22.56 and s = 14.27.

 

The ribeye steak dinners cost $22.56 each and the grilled salmon dinners cost $14.27 each.

 

Note, this solution does not factor in any tips the waitress makes on each dinner!