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

Answer:

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

Step-by-step explanation:

Let

x ----> the number of red circles

y ----> the number of blue circles

Originally

$\frac{x}{y}=\frac{1}{3}$

$y=3x$ ----> 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

$\frac{x+n}{y}=\frac{3}{1}$ ----> equation B

substitute equation A in equation B

$\frac{x+n}{3x}=\frac{3}{1}$

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