ratio problem

**aquajam** · December 4th 2009, 06:28 PM

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!

**skeeter** · December 4th 2009, 06:44 PM

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

**aquajam** · December 4th 2009, 07:42 PM

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

**skeeter** · December 4th 2009, 08:02 PM

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

$x+60 = 2y-120$

$x = 2y-180$

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

$3x-300 = y+100$

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

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

solve for y , then determine x

**aquajam** · December 4th 2009, 08:21 PM

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

Thanks.

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