Question

LINEAR SYSTEM WORD PROBLEM *round answer to the nearest cent*

Answer 1

Drinks, x, and popcorn, y.
125.50 = 12y+7x
87.50=6y+8x

To solve for the cost of drinks, x, isolate the variable
125.50 = 12y + 7x
subtract 12y from both sides
125.50 - 12y = 7x
divide both sides by 7
125.50/7 -12/7y = x

plug that into the other equation
87.50=6y+8x
87.50 = 6y + 8(125.50/7 - 12/7y)
Distribute 8(125.50/7 - 12/7y)
Then combine like terms
then subtract and divide to isolate y
Solve for y
y = 7.25

Plug that into the first equation to solve for x
125.50 = 12y+7x
125.50 = 12(7.25) + 7x
125.50 = 87 + 7x
subtract 87 from both sides
38.5 = 7x
divide both sides by 7
5.5 = x

There, you have the cost of the drinks, $5.5, and the cost of the popcorn, $7.25.

To check: you would plug in what you got for x and y into the original equations and see if they equal right... I did it on paper and it was right!!

Hope this helps