Question

Ome friends went to the local movie theater and bought four large buckets of popcorn and six boxes of candy. The total for the snacks was $46.50. The last time you were at the theater, you bought a large bucket of popcorn and a box of candy, and the total was $9.75. How much would 2 large buckets of popcorn and 3 boxes of candy cost?

Type the price of one bucket of popcorn here.

Type the price of one box of candy here.


How much would 2 large buckets of popcorn cost?

How much would 3 boxes of candy cost?


How much would 2 large buckets of popcorn and 3 boxes of candy cost?

Answer 1

One bucket of popcorn: 6$

One box of candy: $3.75

2 buckets of popcorn: $12

3 boxes of candy: $11.25

2 buckets of popcorn and 3 boxes of candy: $23.25

Explanation:

We can find the cost of one bucket of popcorn and one box of candy using a system of equations

`4P + 6C=46.50\\P + C =9.75`

We can use the elimination method and thus multiply the second equation by -4:

`4P + 6C = 46.50\\-4(P+C=9.75)\\\\4P + 6C = 46.50\\-4P -4C=-39\\\\2C = 7.5\\\\C = 3.75`

We can plug C into the second equation to find P:

`P + 3.75 = 9.75\\P = 6`

Thus, the cost of two buckets of popcorn is 6 * 2 = $12

And the cost of three boxes of candy is 3.75 * 3 = $11.25

And the cost of both two buckets of popcorn and three boxes of candy is (6*2) + (3*3.75) = 12 + 11.25 = $23.25