# 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]$\textcolor{w h i t e}{\text{XXX}} a = \frac{105}{4}$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}