Question

The Miller family visited Mama's Kitchen and ordered 4 hamburgers and 3 medium fries and paid $13.27. James ordered a medium drink, a hamburger, and 2 medium fries and paid $6.33. Steven ordered 2 hamburgers, medium fries, and a medium drink for $7.04. How much did each item cost?
Select one:

a. Each item = $1.61
b. Drink = $1.15, Fries = $1.49, Hamburger = $2.20
c. Drink = $1.49, Fries = $2.20, Hamburger = $1.15
d. Drink = $1.49, Fries = $1.15, Hamburger = $2.20

Answer 1

Let's start out by setting up three separate equations for each customer.
d = cost of drink, f = cost of fries, h = cost of hamburger

Miller Family: 4h + 3f = 13.27
James: d + h + 2f = 6.33
Steven: 2h + f + d = 7.04

Since the Miller's didn't order any drinks, let's start by using substitution to find the cost of d between James and Steven.

Let's isolate d with James:
d + h + 2f = 6.33
d = 6.33 - h - 2f

Now let's plug that into Steven's equation:
2h + f + d = 7.04
2h + f + (6.33 - h - 2f) = 7.04
h - f + 6.33 = 7.04
h - f = 0.71
h = 0.71 + f

Let's plug that new h into the Miller Family's equation:
4h + 3f = 13.27
4(0.71 + f) + 3f = 13.27
2.84 + 4f + 3f = 13.27
2.84 + 7f = 13.27
7f = 10.43
f = 1.49

So medium fries cost $1.49

Let's plug f back into the Miller Family's equation to get h:
4h + 3f = 13.27
4h + 3(1.49) = 13.27
4h + 4.47 = 13.27 
4h = 8.8
h = 2.2

So a hamburger costs $2.20

Let's plug h and f into Steven's equation to calculate d

2h + f + d = 7.04
2(2.2) + (1.49) + d = 7.04
4.4 + 1.49 + d = 7.04
5.89 + d = 7.04
d = 1.15

So a medium drink costs $1.15

The answer is B. Drink = $1.15, Fries = $1.49, Hamburger = $2.20