The sum of two numbers is 45. One of the numbers is two-thirds of the other. What are the two numbers?​

Let's denote the two numbers as \( x \) and \( y \).

Given:
1. The sum of the two numbers is 45: 
   \[
   x + y = 45
   \]
2. One of the numbers is two-thirds of the other. Assuming \( x \) is two-thirds of \( y \):
   \[
   x = \frac{2}{3}y
   \]

Now, we can substitute the expression for \( x \) from the second equation into the first equation:

\[
\frac{2}{3}y + y = 45
\]

To simplify, combine like terms:

\[
\frac{2}{3}y + \frac{3}{3}y = 45
\]

\[
\frac{5}{3}y = 45
\]

Now, solve for \( y \) by multiplying both sides by \( \frac{3}{5} \):

\[
y = 45 \times \frac{3}{5} = 27
\]

With \( y = 27 \), we can find \( x \) using the relationship \( x = \frac{2}{3}y \):

\[
x = \frac{2}{3} \times 27 = 18
\]

So, the two numbers are \( 18 \) and \( 27 \).

### Summary:
- The two numbers are **18** and **27**.

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. What if the sum of the two numbers was 60 instead of 45?
2. How would the solution change if one number was three-quarters of the other?
3. Can you solve the problem using a different method, such as substitution or elimination?
4. What if the problem involved three numbers with a similar relationship?
5. How does this problem relate to ratio and proportion in algebra?

**Tip:** When dealing with word problems, always translate the words into equations and solve step-by-step.

The sum of two numbers is 45. One of the numbers is two-thirds of the other. What are the two numbers?

Discover how to solve a problem where the sum of two numbers is 45, and one number is two-thirds of the other. This solution explores key algebraic concepts, including linear equations and ratio, making it perfect for students in Grades 6-8.

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