Question

A jar contains 10 ounces of gumdrops, 3 ounces of licorice bits, and 3 ounces of jelly beans. How many more ounces of jelly beans must be added to make the assortment 50 percent jelly beans in weight?

Answer 1

10 jelly beans.

Explanation:

Let x be ounces of jelly beans.

We have been given that a jar contains 10 ounces of gumdrops, 3 ounces of licorice bits, and 3 ounces of jelly beans.

To make weight of jelly beans be 50% of total assortment, we will add x ounces of jelly beans to 3 so that it will be 50% of total assortment plus x. We can represent this information in an equation as:

`3+x=(50)/(100)(10+3+3+x)`

Let us solve for x.

`3+x=0.50(16+x)`

`3+x=8+0.5x`

`3-3+x=8-3+0.5x`

`x=5+0.5x`

`x-0.5x=5+0.5x-0.5x`

`0.5x=5`

`(0.5x)/(0.5)=(5)/(0.5)`

`x=10`

Therefore, 10 jelly beans must be added to make the assortment 50 percent jelly beans in weight.

Let us cross check our answer.

`(3+10)/(3+3+10+10)=(13)/(26)=0.5=50\%`