Question

2. Three families bought food at a basketball game. The Davis family spend $16.50 on 3 hotdogs, 2

drinks, and 1 pretzel. The Ruiz family spend $26 on 4 hotdogs, 4 drinks, and 2 pretzels. The Cho family
spend $13.75 on 2 hotdogs, 1 drink, and 3 pretzels. Write a system of equations and solve for the price of each item

Answer 1

x = $3.5

y = $2.25

z = $1.5

Explanation:

let x = price of a hotdog

y = price of a drink

z = price of a pretzel

according to the question:

Davis family spends: 3x+2y+z = $16.50 (equation 1)

Ruiz family spends: 4x+4y+2z = $26 (equation 2)

Cho family spends: 2x+y+3z = $13.75 (equation 3)

from eq. 1

z = 16.50-3x-2y

substituting in eq.2

4x+4y+2(16.50-3x-2y) = 26

4x+4y+33-6x-4y=26

-2x=26-33

thus x = $3.5

from eq. 3

y = 13.75-2x-3z

y = 13.75-2(3.5)-3z

y = 13.75-7-3z

y=6.75-3z

thus,

z = 16.50-3(3.5)-2(6.75-3z)

z = 16.50-10.5-13.5+6z

z-6z = -7.5

-5z = -7.5

thus z = $1.5

thus

y = 6.75-3(1.5)

y = $2.25