Question

Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing

a total of $37.25. Zoe went into the same movie theater and bought 8 bags of popcorn
and 9 pretzels, costing a total of $102.25. Determine the price of each bag of popcorn
and the price of each pretzel.

Answer 1

8 is your answer

Explanation:

Answer 2

A bag of pop corn costs $8, and each Pretzel costs $4.25.

Explanation:

Let
`b` be the price of popcorn, and
`p` the price of Pretzels. If the girl bought 2 bags of popcorn and 5 Pretzels and it cost her $37.25, we have the equation

`2b+5p=37.25` (this says that the cost of 2 popcorn bags plus 5 pretzels equals $37.25) .

And, since Zoe bought 8 popcorn bags and 9 Pretzels with a total price of $102.25, we get the equation

`8b+9p=102.25` (this says that the cost of 8 popcorn bags plus 9 Pretzels equals $102.25).

Thus, we have two equations

1.
`2b+5p=37.25`

2.
`8b+9p=102.25`

and we solve them by first multiplying equation (1) by 4:

`4(2b+5p=37.25 )\rightarrow (8b+20p=149)`,

and then subtracting it from equation (2):

`\:\:\:\:\: 8b+9p=102.25\\-(8b+20p=149)\\\line(1,0){3 cm}\\-11p=-46.75\\\\\boxed{p=\$4.25}`

Now we put this value of
`p` into equation (1) and get:

`2b+5(4.25)=37.25`

and we solve for
`b` to get:

`2b=37.25-21.5`

`\boxed{ b=8}`

Therefore, a bag of popcorn costs $8, and each Pretzel costs $4.25.