# Math Help - ratio problem

1. ## ratio problem

Can this be put into an equation:

Two numbers are such that if the first receives 60 from the second they are in the ratio 2:1, but if the second receives 100 from the first, the ratio is 1:3.

What are the two numbers?

Been experimenting but have gotten far. Thanks!

2. Originally Posted by aquajam
Can this be put into an equation:

Two numbers are such that if the first receives 60 from the second they are in the ratio 2:1, but if the second receives 100 from the first, the ratio is 1:3.

What are the two numbers?

Been experimenting but have gotten far. Thanks!
let x = first number , y = the second

if the first receives 60 from the second they are in the ratio 2:1

$\frac{x+60}{y-60} = \frac{2}{1}$

if the second receives 100 from the first, the ratio is 1:3

$\frac{x - 100}{y + 100} = \frac{1}{3}$

solve the system of equations for x and y

3. Sorry, I'm a bit rusty. Can help me solve it?

4. $\frac{x+60}{y-60} = \frac{2}{1}$

$x+60 = 2y-120$

$x = 2y-180$

$\frac{x - 100}{y + 100} = \frac{1}{3}$

$3x-300 = y+100$

substitute $2y-180$ for $x$ ...

$3(2y-180)-300 = y+100$

solve for y , then determine x

5. I got the x = 2y -180, just didn't what to do next.

Thanks.