Answer:
There were 180 votes for blue.
Step-by-step explanation:
Given:
Riverside elementary school is holding a schoolwide election to choose a color. 5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red.
Now, to find the votes for blue.
Let the total votes be [tex]x.[/tex]
The votes for blue:
[tex]\frac{5}{8} \ of\ x[/tex]
[tex]=\frac{5}{8} \times x[/tex]
[tex]=\frac{5x}{8}[/tex]
Remaining votes are:
[tex]x-\frac{5x}{8} \\\\=\frac{8x-5x}{8} \\\\=\frac{3x}{8}[/tex]
The votes for green:
[tex]\frac{5}{9} \ of\ \frac{3x}{8} \\\\=\frac{5}{9} \times \frac{3x}{8} \\\\=\frac{15x}{72}[/tex]
The remaining votes for red = 48.
Now, the total votes are:
[tex]\frac{5x}{8} +\frac{15x}{72} +48=x\\\\\frac{45x+15x+3456}{72}=x\\\\\frac{60x+3456}{72}=x[/tex]
Multiplying both sides by 72 we get:
[tex]60x+3456=72x[/tex]
Subtracting both sides by 60[tex]x[/tex] we get:
[tex]3456=12x[/tex]
Dividing both sides by 12 we get:
[tex]288=x\\\\x=288.[/tex]
Thus, the total votes = 288.
Now, to get the votes for blue:
[tex]\frac{5}{8} \ of\ 288\\\\=\frac{5}{8}\times 288\\\\=0.625\times 288\\\\=180.[/tex]
Therefore, there were 180 votes for blue.
