# How do you find the two numbers whose ratio is 3 to 4 and that have a sum of 35?

Jul 26, 2016

The two numbers are $\left\{\frac{105}{4} , \frac{35}{4}\right\}$

#### Explanation:

Let the two numbers be $a$ and $b$ such that
[1]$\textcolor{w h i t e}{\text{XXX}} \frac{a}{b} = 3$
and
[2]$\textcolor{w h i t e}{\text{XXX}} a + b = 35$

From [1] (assuming this is a meaningful expression: $b \ne 0$)
we have
[3]$\textcolor{w h i t e}{\text{XXX}} a = 3 b$

Then substituting $3 b$ for $a$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} 3 b + b = 35$
or
[5]$\textcolor{w h i t e}{\text{XXX}} b = \frac{35}{4}$

Combining [3] and [5]
[6]$\textcolor{w h i t e}{\text{XXX}} a = \frac{105}{4}$