Question

A jar has five different colors of gum balls in it. Blue gum balls comprise 20% of the total number of candy. There are 10 more green gum balls than the blue ones. There are half as many red gum balls as blue ones. The ratio of the number of red gum balls to the number of yellow gum balls is 4:7. If the remaining 27.5% of the gum balls are white and one fifth of them were replaced by yellow ones, how many yellow gum balls are there?

Answer 1

46

Explanation:

I go to rsm and the answer worked

Answer 2

Let the total number of gum balls in the jar be x, then the number of blue balls in the jar is 0.2x and the number of green balls is 10 + 0.2x and the number of red balls are 0.5(0.2x) = 0.1x.

Let the initial number of yellow balls in the jar be y, then
`(4)/(7) = (0.1x)/(y) \Rightarrow4y=0.7x\Rightarrow y=0.175x`

The initial number of white balls was 0.275x.

Thus,


`x-0.2x-(10+0.2x)-0.1x-0.175x=0.275x \\ \\ \Rightarrow0.525x-10-0.2x=0.275x \\ \\ \Rightarrow0.325x-0.275x=10 \\ \\ \Rightarrow0.05x=10 \\ \\ \Rightarrow x= (10)/(0.05) =200`

Thus, the initial number of yellow balls was 0.175x = 0.175(200) = 35.
The initial number of white balls was 0.275x = 0.275(200) = 55.
One-fifth of white balls = 1/5(55) = 11.

Therefore, the number of yellow balls in the jar was 35 + 11 = 46.