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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

Respuesta :

mathstudent55

Answer:

$5

Step-by-step 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

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