Question

Two families attended a baseball game. The first family bought 4 bags of popcorn and 5 souvenir cups, which totaled $50. The second family bought 6 bags of popcorn and 4 souvenir cups, which totaled $54. How much did one bag of popcorn cost? $4 $5 $6 $7

Answer 1

$5

Explanation:

I took the test

hypothetically, say the popcorn WAS 5 dollars. 5x4 = 20

$50 - $20 = 30 that makes the souvenirs $6 because 30/5 = 6.

If we use this for the next family, 5x6 is 30 for the popcorn plus 6x4 for the souvenirs totals at 54 making this equation correct.

Answer 2

$5

Explanation:

Let x = price of 1 bag of popcorn.

Let y = price of 1 souvenir cup

First family:

4x + 5y = 50

Second family:

6x + 4y = 54

We have a system of 2 equations with 2 variables.

4x + 5y = 50

6x + 4y = 54

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

Multiply both sides of the first equation by -4. Multiply both sides of the second equation by 5.

-16x - 20y = -200

30x + 20y = 270

Add the equations to eliminate y.

14x = 70

x = 70/14

x = 5

Answer: $5