# Ratio and Proportion. The bigger plus two times the smaller number is equal to 42

• Feb 25th 2011, 08:55 PM
lucas7
Ratio and Proportion. The bigger plus two times the smaller number is equal to 42
The ration between 2 numbers is $\displaystyle -\frac{3}{8}$. If the bigger numer plus two times the smaller number is equal to 42, find out the bigger number value.

$\displaystyle \frac{x}{y} = -\frac{3}{8}$

$\displaystyle -3y=8x$
$\displaystyle y = -\frac{8x}{3}$ $\displaystyle x = \frac{-3y}{8}$

How do I find out which one is the bigger? obviously 3 is smaller than 8, but, couldn't it be the number 3 positive and the number 8 negative, therefore number 3 could be bigger than 8?

Thanks for the help in advance.
• Feb 25th 2011, 09:17 PM
sa-ri-ga-ma
For the time being forget the negative sign.

Let the fraction be $\displaystyle \frac{3x}{8x}$

Here 8x is greater than 3x. Now proceed.
• Feb 25th 2011, 09:33 PM
lucas7
$\displaystyle x = -\frac{3y}{8}$

$\displaystyle y+2x=42$

$\displaystyle y+2.\frac{-3y}{8}=42$

$\displaystyle y=168$

Thats the answer, but still didn't understand how could I know for SURE which one is bigger.
• Feb 25th 2011, 09:55 PM
sa-ri-ga-ma
While considering the ratio you have to consider whether it is more than 1 or less than 1. From that you have decide which number is larger. You should not place the numbers on the number line to decide which one is larger.