Question

Easton and Eli go to the movie theater and purchase refreshments for their friends.

Answer 1

For this case we have to:

x: Let the variable that represents the cost of a bag of popcorn

y: Let the variable that represents the cost of a drink

According to the statement we have:

$9x + 6y = 118.59\\3x + 10y = 83.50$

We multiply the second equation by -3:

$-9x-30y = -250.5$

We have the following equivalent system:

$9x + 6y = 118.59\\-9x-30y = -250.5$

We add:

$9x-9x + 6y-30y = -131.91\\-24y = -131.91\\y = \frac {131.91} {24}\\y = 5.496$

Thus, each drink costs $5,496

On the other hand:

$x = \frac {118.59-6 (5,496)} {9}\\x = \frac {118.59-32.976} {9}\\x = 9.51$

Thus, each bag of popcorn costs $9.51

Answer:

$9x + 6y = 118.59\\3x + 10y = 83.50$

Each bag of popcorn costs $9.51