How much did they cost???

Question

A waitress sold 10 ribeye steak dinners and 33 grilled salmon dinners, totaling $587.92on a particular day. Another day she sold 26 ribeye steak dinners and 11 grilled salmon dinners, totaling $581.71. How much did each type of dinner cost?

Answer 1

Hi,

Write mathematical representations in an equation form and solve as a system of equations.

 

Equation 1: 10R + 33G = 587.92

Equation 2: 26R + 11G = 581.71

 

Use linear combination method

Step 1: Multiply Equation 2 by 3 on both sides 

3(26R + 11G) = 3(581.71)

   78R + 33G  = 1745.13

Step 2: Subtract. Equation 2 - Equation 1

  78R + 33G = 1745.13

-(10R + 33G = 587.92)

   68R + 0 = 1157.21

Step 3:SOLVE        R = 17.02

26(17.02) +11G = 581.71

                     G = 12.65

The answer is the ribeye steak dinner costs $17.02 and the grilled salmon dinner costs $12.65 each.