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

1. 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.

2. For the time being forget the negative sign.

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

Here 8x is greater than 3x. Now proceed.

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

$\displaystyle y+2x=42$

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

$\displaystyle y=168$

Thats the answer, but still didn't understand how could I know for SURE which one is bigger.

4. 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.