Answer:
A bag of pop corn costs $8, and each Pretzel costs $4.25.
Step-by-step explanation:
Let [tex]b[/tex] be the price of popcorn, and [tex]p[/tex] 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
[tex]2b+5p=37.25[/tex] (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
[tex]8b+9p=102.25[/tex] (this says that the cost of 8 popcorn bags plus 9 Pretzels equals $102.25).
Thus, we have two equations
1. [tex]2b+5p=37.25[/tex]
2. [tex]8b+9p=102.25[/tex]
and we solve them by first multiplying equation (1) by 4:
[tex]4(2b+5p=37.25 )\rightarrow (8b+20p=149)[/tex],
and then subtracting it from equation (2):
[tex]\:\:\:\:\: 8b+9p=102.25\\-(8b+20p=149)\\\line(1,0){3 cm}\\-11p=-46.75\\\\\boxed{p=\$4.25}[/tex]
Now we put this value of [tex]p[/tex] into equation (1) and get:
[tex]2b+5(4.25)=37.25[/tex]
and we solve for [tex]b[/tex] to get:
[tex]2b=37.25-21.5[/tex]
[tex]\boxed{ b=8}[/tex]
Therefore, a bag of popcorn costs $8, and each Pretzel costs $4.25.
