Question

A group of 40 children attended a baseball game on a field trip. Each child received either a hot dog or a bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hot dogs and bags of popcorn were purchased?

Answer 1

I found:
`27` hot dogs
`13` bags of popcorn

Explanation:

Call the number of hot dogs `h` and popcorn `p`;
you have:
`{(h+p=40),(2.25h+1.75p=83.5):}`
from the first you have:
`h=40-p` substitute into the second:
`2.25(40-p)+1.75p=83.5`
`90-2.25p+1.75p=83.5` rearranging:
`0.5p=6.5`
`p=6.5/0.5=13`
substitute back into: `h=40-p`
`h=40-13=27`