Question

Juan and his children went into a movie theater and he bought $52.50 worth of bags of popcorn and pretzels. Each bag of popcorn costs $7.50 and each pretzel costs $3.75. He bought 5 more pretzels than bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Juan bought.

Answer 1

Juan bought 3 bags of popcorn and 8 bags of pretzel

Explanation:

Given

`x = popcorn`

`y = pretzels`

`Amount = \$52.50`

Required

Solve graphically

First, we need to represent the cost as an equation.

If popcorn costs 7.50 per bag and pretzel costs 3.75 per bag

The cost is then represented as:

`7.50x + 3.75y = 52.50`

Next, we represent the quantity as an equation.

Bags of pretzel is 5 more than bags of popcorn

The quantity is then represented as:

`y = x + 5`

At this stage, we have:

`7.50x + 3.75y = 52.50`

`y = x + 5`

See attachment for graph

`7.50x + 3.75y = 52.50` is represented by the
`green\ line` while the
`blue\ line`represents
`y = x + 5`

At the point of intersection of both lines, we have:

`(x,y) = (3,8)`

This implies that;

Juan bought 3 bags of popcorn and 8 bags of pretzel