Question

what equashion can be used to find two numbers those ratio are 3 to 2 and have the sum of 35

Answer 1

We need to set up a system, rather than a single equation, because there are two variables involved.

The first equation represents the fact that the two numbers are in a 3:2 ratio:

$\dfrac{x}{y}=\dfrac{3}{2} \iff x=\dfrac{3}{2}y$

The second equation represents the fact that their sum is 35:

$x+y=35$

So, we have the following system:

$\begin{cases}x = \dfrac{3}{2}y\\x+y=35\end{cases}$

Using the expression for x in the first equation, the second one becomes

$x+y=35 \iff \dfrac{3}{2}y+y=35 \iff\dfrac{5}{2}y=35 \iff 5y=70 \iff y = 14$

which implies

$x=35-y=35-14=21$