Help me figure out this math problem

Question

a club collected $84 to pay the exact cost of 20dinners. Some had order beef diner at $4.50 Each. And some had ordered the fish dinner at $3.75each. How many dinners of each kind were ordered? 

Answer 1

X = number of $4.50 dinners

 

Y = number of $3.75 dinners

 

                        X + Y = 20     total of 20 dinners

 

      $4.50X + $3.75Y = $84   value of dinners totaled $84

 

Multiply second equation by 100 to clear the decimals

 

          450X + 375Y = 8400

 

                      X + Y = 20       Multiply by -450

 

          -450X - 450Y = -9000  Combine the two equations

 

                     - 75Y  = -600

 

                            Y = 8

 

8 of $3.75 dinners and 12 of $4.50 dinners