Question

2. Riverside Elementary School is holding a school-wide election to choose a school color. Five-eighths of the votes were for blue, 5/9 of the remaining votes were for green, and the remaining 48 votes were for red.

a. How many votes were for blue?



b. How many votes were for green?

Answer 1

a. 180 votes were for blue

b. 60 votes were for green

Explanation:

Fractions

It's known 5/8 of the votes of a school-wide election were for painting the school blue. Suppose there were x voters in school.

Since 5/8 were for blue, then

`1-(5)/(8)=(3)/(8)`

Were for the rest of the colors. It's also known 5/9 of the remaining votes were for green, thus

`1-(5)/(9)=(4)/(9)`

of the remaining votes were for red.

The votes for red are:

`(3)/(8)\cdot(4)/(9)=(1)/(6)`

of the total voters.

We know these were 48 votes, thus

`\displaystyle x=(48)/((1)/(6))`

`x = 288`

There were 288 voters in school.

a. 5/8 were for blue, that is:

`(5)/(8)*288=180`

180 votes were for blue

b. 288-180 = 108 votes were for others than blue, and 5/9 of them were for green:

`(5)/(9)*108=60`

60 votes were for green and 108-60=48 votes were for red (as expected)