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

There were 180 votes for blue.

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:

`(5)/(8) \ of\ x`

`=(5)/(8) * x`

`=(5x)/(8)`

Remaining votes are:

`x-(5x)/(8) \\\\=(8x-5x)/(8) \\\\=(3x)/(8)`

The votes for green:

`(5)/(9) \ of\ (3x)/(8) \\\\=(5)/(9) * (3x)/(8) \\\\=(15x)/(72)`

The remaining votes for red = 48.

Now, the total votes are:

`(5x)/(8) +(15x)/(72) +48=x\\\\(45x+15x+3456)/(72)=x\\\\(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:

`(5)/(8) \ of\ 288\\\\=(5)/(8)* 288\\\\=0.625* 288\\\\=180.`

Therefore, there were 180 votes for blue.