Need 3 equations & solution

Question

your company reach it sales goals for the year so you decided to buy dinner for 45 employees the restaurant gives you chicken dinners at $9 each, salmon dinners at $12 each and steak dinners at $15 each. The total number of chicken dinners you ordered is half of the sum of the number of salmon and steak. If you spend total of $525. how many types of each dinner you bought?

Answer 1

# of chicken dinners is C

# of salmon dinners is F (for fish)

# of steak dinner is S

 

C = (F +S)/2 ---> 2C - F - S = 0

 

C + F + S = 45

 

9C + 12F + 15S = 525

 

 

Adding the first two equations together:

 3C = 45

C = 15 ;   so 15 chicken dinners ordered

Substituting this into the equations:

  F + S = 30 --> S = 30 - F

 

9(15) + 12F + 15S = 525

135 + 12F + 15S = 525

12F + 15S = 390

4F + 5S = 130

 

4F + 5(30 - F) = 130

4F + 150 - 5F = 130

 

 -F = 130 - 150

-F = -20

F = 20

 

So 20 salmon fish dinners ordered.

 

That leaves 10 steak dinners ordered,

as they must total 45 altogether.

 

Indeed 15 = (20+10)/2 = 30/2

 

and

 

9*15 + 12*20 + 15*10 =

135 + 240 + 150 =

375 + 150 =

525

 

15 chicken dinners

20 salmon fish dinners

10 steak dinners