Question

Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the voters were for blue 5/9 of the remaining voters were for green. And the remaining 48 voters were for red. How many voters were for blue?

Answer 1

There were 180 voters for blue color.

Explanation:

Let the total number of voters be 'x'.

Given:

Number of Voters for blue color =
`(5)/(8)x`

Number of Voters for green color =
`(5)/(9)(x-\frac58x)=\frac59x(1-\frac58)`

Now we will use LCM to make the denominator common we get;

Number of Voters for green color =
`\frac59x(\frac88-\frac58)=\frac59x((8-5)/(9))=\frac59x(\frac38)=(15x)/(72)`

Number of Voters for red color = 48

We need to find the number of voters for blue color.

Solution:

Now we can say that;

total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.

framing in equation form we get;

`x=\frac58x+(15x)/(72)+48`

Combining like terms we get;

`x-\frac58x-(15x)/(72) = 48`

Now we will make denominators common using LCM we get;

`(72x)/(72)-(5x*9)/(8*9)-(15x*1)/(72* 1) = 48\\\\(72x)/(72)-(45x)/(72)-(15x)/(72) = 48`

Now denominators are common so we will solve the numerators we get;

`(72x-45x-15x)/(72)=48\\\\(12x)/(72)=48\\\\(x)/(6)=48`

Now multiplying both side by 6 we get;

`(1)/(6)x*6=48*6\\\\x = 288`

Number of voters for blue color =
`(5)/(8)x=(5)/(8)* 288= 180`

Hence There were 180 voters for blue color.