Question

A juice company sells its product in either a 48-ounce size or a 32-ounce size. It charges $\$3.90$ for the 48-ounce size. How much should it charge for the smaller size if it wants the price per ounce to be $25\%$ more than the price per ounce of the larger size?

Answer 1

3.25

Explanation:

We could solve this problem by figuring out the per-ounce cost of the 48-ounce package, increasing it by $25\%$, and then multiplying that by 32 for the smaller package. However, if we simply increase the price by $25\%$, and then scale the package size down to 32 ounces from 48 ounces, these are the same calculations, but in a different order that makes it easier to calculate. Thus: $3.90 \times 1.25 \times \frac{32}{48} = \boxed{3.25\text{ dollars}}$

Answer 2

The company should charge $ 3.25 for the smaller size.

Explanation:

The price per ounce of the 32-ounce product is required to be 25% greater than the larger-sized product.

We know that for the size of 48 ounces the price is $ 3.90

So, the price per ounce is:

`(3.90)/(48)`= $ 0.08125

For the smallest size the price per ounce should be 25% higher.

So:

$ 0.08125 (1 + 0.25) = $ 0.10156

The total price for the smallest size is:

$ 0.10156 * 32 = $ 3.25

The company should charge $ 3.25 for the smaller size.