Question

Katy bought 22 butterscotch candies. The candies came in bags, and the number of bags was 9 less than the number of candies in each bag. How many bags of candy did Katy buy?

Answer 1

2 bags

Explanation:

Let the number of bags be b.

Let the number of candies in each bag be c.

The number of bags was 9 less than the number of candies in each bag. That is:

b = c - 9

She bought 22 candies.

This means that The number of candy in each bag multiplied by the numbe of each bag is 22:

b * c = 22

bc = 22

=> (c - 9) * c = 22

`c^2 - 9c = 22\\\\c^2 - 9c - 22 = 0\\\\c^2 - 11c + 2c - 22 = 0\\\\c(c - 11) + 2(c - 11) = 0\\\\(c + 2) (c - 11) = 0\\\\=> c = -2, c = 11`

Since the number of candies can only be a positive number, c = 11.

Therefore:

b = 11 - 9

b = 2

Katy bought 2 bags of candy containing 11 candies each.