Question

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.How many votes were for blue

Answer 1

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 $x.$

The votes for blue:

$\frac{5}{8} \ of\ x$

$=\frac{5}{8} \times x$

$=\frac{5x}{8}$

Remaining votes are:

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

The votes for green:

$\frac{5}{9} \ of\ \frac{3x}{8} \\\\=\frac{5}{9} \times \frac{3x}{8} \\\\=\frac{15x}{72}$

The remaining votes for red = 48.

Now, the total votes are:

$\frac{5x}{8} +\frac{15x}{72} +48=x\\\\\frac{45x+15x+3456}{72}=x\\\\\frac{60x+3456}{72}=x$

Multiplying both sides by 72 we get:

$60x+3456=72x$

Subtracting both sides by 60$x$ we get:

$3456=12x$

Dividing both sides by 12 we get:

$288=x\\\\x=288.$

Thus, the total votes = 288.

Now, to get the votes for blue:

$\frac{5}{8} \ of\ 288\\\\=\frac{5}{8}\times 288\\\\=0.625\times 288\\\\=180.$

Therefore, there were 180 votes for blue.