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:

`(x)/(y)=(3)/(2) \iff x=(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 = (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 (3)/(2)y+y=35 \iff(5)/(2)y=35 \iff 5y=70 \iff y = 14`

which implies

`x=35-y=35-14=21`