Question

3) When Jackie took her children to the movie theater, she bought one box of candy and three small drinks for

$14.75. When Alex went to the same theater and bought two boxes of candy and five small drinks, he paid
$26.
a) Set up a system of equations to model this situation. Be sure to define the variables that you use.
b) Determine, algebraically, the cost for one box of candy and one small drink

Answer 1

c + 3d = 14.75

2c + 5d = 26

A box of candy is $4.25 and a drink is $3.50

Explanation:

Let c represent the cost of a box of candy and let d represent the cost of a drink

c + 3d = 14.75

2c + 5d = 26

Solve by elimination by multiplying the top equation by -2

-2c - 6d = -29.5

2c + 5d = 26

Add them together

-d = -3.5

d = 3.5

Plug in 3.5 as d into one of the equations to solve for c

c + 3d = 14.75

c + 3(3.5) = 14.75

c + 10.5 = 14.75

c = 4.25

So, a box of candy is $4.25 and a drink is $3.50