The sum of two numbers, one of which is two-thirds of the other, is 45. Find the smaller number:

🧠 Explanation:

Let the two numbers be $x$ and $y$, where one is two-thirds of the other.

Given that $y = \frac{2}{3}x$ (assuming $y$ is the smaller number).

Their sum is 45, so:

$$
x + y = 45
$$

Substitute $y$:

$$
x + \frac{2}{3}x = 45
$$

Combine like terms:

$$
\frac{3}{3}x + \frac{2}{3}x = 45
$$

$$
\frac{5}{3}x = 45
$$

Multiply both sides by 3:

$$
5x = 135
$$

Divide both sides by 5:

$$
x = 27
$$

Now find $y$:

$$
y = \frac{2}{3} \times 27 = 18
$$

So, the smaller number is **18**.