Question

I have a question. if a number is 2/3 of another number and the sum of the two numbers is 30, how can I set this up to find the smaller number?

Answer 1

ANSWER

Solving this system for x,

$\begin{cases}x=\frac{2}{3}y \\ x+y=30\end{cases}$

EXPLANATION

We have two numbers. Let them be x and y. We know that one of them is 2/3 of the other, so this makes one equation,

$x=\frac{2}{3}y$

And we also know that the sum of these two numbers is 30, so we have another equation,

$x+y=30$

To find the smaller number we would solve this system for x,

$\begin{cases}x=\frac{2}{3}y \\ x+y=30\end{cases}$

From the first equation, we know that x represents the smaller number.