# Ratio Proportion

• Dec 3rd 2011, 10:57 AM
MoniMini
Ratio Proportion
I'm stuck up with this too (Doh)

Quote:

The ages of Katheline and Gwen are in the ratio 2 : 3. After 12 years, their ages will be in the ratio 11 : 15. The age of Gwen is-
a) 32 years
b) 42 years
c) 48 years
d) 56 years
(Worried)
Any help will be appreciated.

Thanks a Lot!
• Dec 3rd 2011, 11:16 AM
earboth
Re: Ratio Proportion
Quote:

Originally Posted by MoniMini
I'm stuck up with this too (Doh)

(Worried)
Any help will be appreciated.

Thanks a Lot!

Let x denote the age of Katheline and y the age of Gwen.

Then you know:

$\frac xy = \frac23$

$\frac{x+12}{y+12} = \frac{11}{15}$

This is a system of simultaneous equations which you can solve easily.
• Dec 3rd 2011, 06:03 PM
MoniMini
Re: Ratio Proportion
Ok.......
Initially I had come to this conclusion but
I'm having some troubles after this equation.
How to find the values of x and y?
• Dec 3rd 2011, 07:41 PM
mathbyte
Re: Ratio Proportion
Usually in solving a system of simultaneous equations, you wind up manipulating one of them so you can express on variable in terms of the other. That allows you to substitute that variable into the other equation.

Let's take this instance as an example: let's call the top equation Equation 1, and the lower one Equation 2.

Equation 1 can be re-worked so we can express x in terms of y:

x/y = 2/3

3x = 2y

So we can then figure out

x = 2y/3

Knowing that, we can then substitute this value for x into Equation 2. When you do that, what do you get then?
• Dec 4th 2011, 12:21 AM
MoniMini
Re: Ratio Proportion [SOLVED]
Oooh! I got it now!
$\frac xy = \frac23$
and
$\frac{x+12}{y+12} = \frac{11}{15}$

then

$\15 (x + 12) = 11 (y + 12)$

$= 15x + 180 = 11y + 132$

$= 180 - 132 = 11y - 15x$

$= 48 = 11y - 15x$

and if

$\frac xy = \frac23$

then

$x = \frac {2y} 3$

then

$15x = \frac {15} 1 \!\cdot\! \frac {2y} 3$
$= \frac {30y}3$

then we go back to

$= 48 = 11y - 15x$

so that becomes

$48 = 11y - \frac {30y}3$
$= 48 = 11y - 10y$
$= 48 = y$

So, if $x$ is Katheline and $y$ is Gwen, then
Gwen is 48 years old.

Whoa!!
Thnx a lot @earboth and @mathbyte!

~MoniMini