$28.20 for 3 small dishes and 5 large dishes $23.30 for 4 small dishes and 3 large dishes. what will 2 small and 4 large dishes cost

Question

a restaurant charged one customer $28.20 for 3 small dishes and 5 large dishes and charged another customer $23.30 for 4 small dishes and 3 large dishes. what will 2 small and 4 large dishes cost

Answer 1

 

Let x = cost for a small dish

Let y = cost of a large dish

 

   3x + 5y = 28.20

   4x + 3y = 23.30

 

Use Elimination method to solve the system.

We need opposite coefficiients for one of the variables.

Lets multiply equation one by 4, and equation 2 by -3.

Then we add the 2 equations, eliminate variable x,

 

   12x + 20y =  112.8

  -12x  -   9y =   -69.9

 ---------------------------------

              11y = 42.9

                

                 y = 3.90

 

Take equation 1, susbstitute in the  above value of y, and solve for x

 

    3x + 5y = 28.20

    3x + 5(3.9) = 28.20

    3x + 19.5 = 28.20

               3x = 8.70

                 x = 2.90

 

The small plate costs $2.90

The large plate costs $3.90