Two families attended a baseball game. The first family bought 5 bags of popcorn and 6 souvenir cups, which totaled $65. The sec

Question

1 year ago

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Two families attended a baseball game. The first family bought 5 bags of popcorn and 6 souvenir cups, which totaled $65. The sec

ond family bought 10 bags of popcorn and 4 souvenir cups, which totaled $90. How much did one bag of popcorn cost?
$4
$5
$6
$7

Mathematics

1 answer:

Bumek [7] · Answer 1 · 2023-12-24T05:23:55+03:00

The cost of one bag is given as

$5

<h3> How much did one bag of popcorn cost?</h3>

Generally, the equation for the First family is mathematically given as

4x + 5y = 50

Equation Second family:

6x + 4y = 54

We have a system of 2 equations with 2 variables.

4x + 5y = 50

6x + 4y = 54

Since we are being asked for the cost of one bag of popcorn, which we will refer to as x, we will first remove y and then proceed to find x.

Both sides of the first equation need to be multiplied by -4, and both sides of the second equation need to be multiplied by 5. We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

-16x - 20y = -200

30x + 20y = 270

In conclusion, Simply adding the equations will get rid of y.

14x = 70

x = 70/14

x = 5