Question

The sum of the two numbers is 208. One-third of the greater number equals the smaller number. What are the numbers?

Answer 1

Let the two numbers be x and y.

The sum is equal to 208:

$x+y=208$

It is given that one-third of the greater number equals the smaller number. If x is the smaller number, we have that:

$\begin{gathered} \frac{y}{3}=x \\ \therefore \\ y=3x \end{gathered}$

Therefore, the two numbers can be x and 3x, and the sum will be:

$\begin{gathered} x+3x=208 \\ \therefore \\ 4x=208 \\ x=52 \end{gathered}$

If the smaller number is 52, then the larger number will be:

$3\times52=156$

The two numbers are 52 and 156.