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
[tex]1-\frac{5}{8}=\frac{3}{8}[/tex]
Were for the rest of the colors. It's also known 5/9 of the remaining votes were for green, thus
[tex]1-\frac{5}{9}=\frac{4}{9}[/tex]
of the remaining votes were for red.
The votes for red are:
[tex]\frac{3}{8}\cdot\frac{4}{9}=\frac{1}{6}[/tex]
of the total voters.
We know these were 48 votes, thus
[tex]\displaystyle x=\frac{48}{\frac{1}{6}}[/tex]
[tex]x = 288[/tex]
There were 288 voters in school.
a. 5/8 were for blue, that is:
[tex]\frac{5}{8}*288=180[/tex]
180 votes were for blue
b. 288-180 = 108 votes were for others than blue, and 5/9 of them were for green:
[tex]\frac{5}{9}*108=60[/tex]
60 votes were for green and 108-60=48 votes were for red (as expected)
