Question

In this line of circles, the ratio of red circles to blue circles is 1:3 How many more circles would need to be added to make the ratio of red to blue 3:1

Answer 1

The number of red circles to be added would be equal to 8 times the original amount of red circles

Explanation:

Let

x ----> the number of red circles

y ----> the number of blue circles

Originally

`(x)/(y)=(1)/(3)`

`y=3x` ----> equation A

How many more circles would need to be added to make the ratio of red to blue 3:1

Let

n ----> the number of additional red circles

`(x+n)/(y)=(3)/(1)` ----> equation B

substitute equation A in equation B

`(x+n)/(3x)=(3)/(1)`

solve for n

`x+n=9x\\n=9x-x\\n=8x`

therefore

The number of red circles to be added would be equal to 8 times the original amount of red circles