Two numbers are in the ratio 4:5. If they add up to 180, what are the two numbers? 

Given that the two numbers are in the ratio \(4:5\) and their sum is \(180\), we can solve for the individual numbers.

Let the two numbers be \(4x\) and \(5x\), where \(x\) is a common multiplier.

According to the problem:

\[
4x + 5x = 180
\]

Simplifying:

\[
9x = 180
\]

Now, solve for \(x\):

\[
x = \frac{180}{9} = 20
\]

Thus, the two numbers are:

\[
4x = 4 \times 20 = 80
\]
\[
5x = 5 \times 20 = 100
\]

So, the two numbers are **80** and **100**.

Would you like details on the method used, or do you have any other questions?

Here are 5 related questions you might find interesting:
1. What would the numbers be if they were in the ratio \(3:4\) and added up to \(140\)?
2. How do you determine the ratio of two numbers if their sum and difference are known?
3. What if the ratio was \(7:9\) and the sum was \(256\)?
4. How can you generalize the process to find numbers given any ratio and sum?
5. How do ratios work in real-world problems involving proportions?

**Tip:** When solving ratio problems, always express the numbers in terms of a common variable to simplify calculations.

Learn how to solve a ratio problem where two numbers are in the ratio 4:5 and their sum is 180. This problem involves applying ratio and proportion concepts, suitable for Grades 7-9 students.

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