How many of each meal was ordered?

Question

For a small party of 12 people, the caterer offered a choice of a steak dinner for $12.00 per meal or a chicken dinner for $10.50 per meal. The final cost for the meals was $138.00. How many of each meal was ordered?

Answer 1

The total number of meals was 12:  x + y = 12

The total cost was 138:  12x + 10.50y = 138      x is the number of steak dinners an y the number of chicken dinners.

 

The system:          x + y = 12

                 12x + 10.50y = 138

 

If you use the elimination method you can multiply the first equation by 12:    12x + 12y = 144

 

Then subtracting the second equation from this equation gives you:      12x + 12y = 144

                                                                                                  -(12x + 10.50y = 138)

                                                                                                      0x + 1.50y  = 6

                                                                       dividing by 1.50:                     y = 4

 

Using the first equation x + y = 12, replace y with it's value of 4 and solve for x:    x + 4 = 12.

                                                                                                                             x = 8

 

There were 8 steak dinners and 4 chicken dinners ordered.

 

Check:    8 + 4 = 12  and 8(12) + 4(10.50) = 138

 

 

Answer 2

 

Hi Lindsey,

 

Assuming one meal has been ordered for each person,

 

let x and y represent the number of steaks and the number of chickens ordered, respectively.

 

Then, we get the following system of linear equations.

 

     x + y = 12               (Eq. 1)

 

     12x + 10.5y = 138   (Eq. 2)

 

If we plug y = 12 - x, which is from Eq. 1, into Eq. 2,

 

     12x + 10.5(12 - x) = 138

 

     1.5x + 126 = 138

 

     1.5x = 12

 

     x = 8

 

and plug x = 8 into Eq. 1,

 

we get y = 4.

 

So, they ordered 8 steaks and 4 chickens.