Question

At the movies jodie buys three regular popcorns and five small drinks for her friends at a cost of $24.50 her friend renee buyd four regular popcorns and three small drinks for her friends at a cost of $23.50 find the individual costs of a regular popcorn and a small drink

The final answer should be a regular popcorn is $4 and a small drink is $2.50 but I have no idea how to get that answer. Can someone please explain?

Answer 1

Explanation:

Let

Cost of popcorn = x

Cost of drink = y

3x + 5y = 24.5(1)

4x + 3y = 23.5(2)

From 1

3x + 5y = 24.5

3x = 24.5 - 5y

x = (24.5 - 5y)/3

Putting value of x in 2

4(24.5 - 5y)/3 + 3y = 23.5

98 - 20y/3 + 3y = 23.5

98 - 20y + 9y/3 = 23.5

98 - 11y = 3 × 23.5

98 - 11y = 70.5

-11y = 70.5 - 98.5

-11y = -28

y = 2.5

3x + 5(2.5) = 24.5

3x + 12.5 = 24.5

3x = 24.5 - 12.5

3x = 12

x = 12/3

x = 4