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

Answer:

a. 180 votes were for blue

b. 60 votes were for green

Step-by-step 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

$1-\frac{5}{8}=\frac{3}{8}$

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

$1-\frac{5}{9}=\frac{4}{9}$

of the remaining votes were for red.

The votes for red are:

$\frac{3}{8}\cdot\frac{4}{9}=\frac{1}{6}$

of the total voters.

We know these were 48 votes, thus

$\displaystyle x=\frac{48}{\frac{1}{6}}$

$x = 288$

There were 288 voters in school.

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

$\frac{5}{8}*288=180$

180 votes were for blue

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

$\frac{5}{9}*108=60$

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