Question

Maggie makes and sells scented body lotions. She initially spent 108 to purchase supplies, and each kilogram of lotion cost 16 to make. Maggie sells the lotion for 25 per kilogram. How many kilograms of lotion will Maggie have to sell to break even?

Answer 1

12 kilograms

Explanation:

Let's construct an equation for her profits, we will call it P(x), where x is the number of kilograms produced/sold.

We know she has -$108 profit from buying supplies, and for each kilogram she produces, she earns -$16 (or loses $16, if earning negative money bothers you). However, we also know that she earns $25 per kilogram sold.

Constructing the equation with this information, we get:
`P(x)=25x-16x-108=9x-108`

Setting this equation to zero and solving for x:

`9x-108=0`

`9x=108`

`x=12`