the ratio of students to professionals in a conference is 4:5. If there are 45 participants altogether, how many are professionals

Given the ratio of students to professionals as 4:5, and knowing there are 45 participants in total, we can find the number of professionals by following these steps:

1. **Express the ratio in terms of variables:**
   - Let the number of students be \(4x\).
   - Let the number of professionals be \(5x\).

2. **Set up an equation for the total number of participants:**

\[
4x + 5x = 45
\]

3. **Combine like terms:**

\[
9x = 45
\]

4. **Solve for \(x\):**

\[
x = \frac{45}{9} = 5
\]

5. **Find the number of professionals:**

\[
\text{Number of professionals} = 5x = 5 \times 5 = 25
\]

So, there are **25 professionals** at the conference.

Do you have any questions or need further details?

Here are five related questions for further practice:
1. If the ratio was 3:2 and there were 60 participants, how many would be professionals?
2. What if the ratio was 7:3 and there were 80 participants in total?
3. How many students would there be if the ratio was 5:6 and there were 66 participants?
4. If 60 participants were at the conference with a ratio of 4:5, how many more professionals than students would there be?
5. If 10 more participants joined, all of whom were students, how would the ratio change?

**Tip:** When working with ratios, always remember to add the parts of the ratio to form the total parts, then solve for the variable.

Learn how to calculate the number of professionals in a conference based on the given ratio of students to professionals and total participants. Practice with similar problems involving ratios and total counts. Suitable for Grades 6-8.

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