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

Answer:

10 jelly beans.

Step-by-step 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:

$3+x=\frac{50}{100}(10+3+3+x)$

Let us solve for x.

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

$3+x=8+0.5x$

$3-3+x=8-3+0.5x$

$x=5+0.5x$

$x-0.5x=5+0.5x-0.5x$

$0.5x=5$

$\frac{0.5x}{0.5}=\frac{5}{0.5}$

$x=10$

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

Let us cross check our answer.

$\frac{3+10}{3+3+10+10}=\frac{13}{26}=0.5=50\%$