Q:

4 specials and 2 glasses of milk = $28.00. 3 specials and 4 glasses of milk = $26.25. How much does it cost for 2 specials and 2 glasses of milk?

Accepted Solution

A:
First, we should write the equation system of the problem
s stands for special, m stands for milk
⇒ 4s + 2m = 28.00 (first equation)
⇒ 3s + 4m = 26.25 (second equation)

Solve the first and second equation using elimination method. I'm going to eliminate m, so we can calculate s.
4s + 2m = 28.00 (multiply 2)
3s + 4m = 26.25 (multiply 1)
-------------------------------------
8s + 4m = 56.00
3s + 4m = 26.25
----------------------- - (substract)
5s          = 30.25
s            = 6.05

I'm using subtitution method to find m. Subtitute 6.05 as s to one of the equation.
4s + 2m = 28.00
4(6.05) + 2m = 28.00
24.20 + 2m = 28.00
2m = 3.80
m = 1.90

The cost for a glass of milk is $1.90 and a special is $6.05

Calculate cost for 2 specials and 2 glasses of milk
2s + 2s
= 2(6.05) + 2(1.90)
= 12.10 + 3.80
= 15.90

The cost for 2 specials and 2 glasses of milk is $15.90