Question

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

Answer 1

Answer:

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

Step-by-step 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.