The ratio of hockey players to badminton players in a particular school is 10:7. If there are 70 hockey players in the school, then how many badminton players are in the school?




Given that the ratio of hockey players to badminton players is 10:7, and there are 70 hockey players, we can find the number of badminton players using the following steps:

1. **Set up the ratio:**
   \[
   \frac{\text{Hockey players}}{\text{Badminton players}} = \frac{10}{7}
   \]

2. **Express the ratio as a proportion:**
   \[
   \frac{10}{7} = \frac{70}{x}
   \]
   Where \( x \) represents the number of badminton players.

3. **Solve for \( x \):**
   \[
   x = \frac{7 \times 70}{10}
   \]

   \[
   x = \frac{490}{10} = 49
   \]

So, there are **49 badminton players** in the school.

Would you like to dive into more details or ask another question?

Here are some related questions you might find interesting:

1. If there were 105 badminton players, how many hockey players would there be?
2. What is the total number of students involved in either hockey or badminton?
3. If 30 more students joined hockey, how would that affect the ratio?
4. How would you calculate the number of hockey players if the total number of players was given?
5. What if the ratio changed to 5:3 but the number of hockey players stayed the same?
6. How does the ratio help in predicting the number of players for each sport?
7. If 14 badminton players leave the school, what happens to the new ratio?
8. How many more hockey players are there compared to badminton players?

**Tip:** Ratios can be used to easily scale quantities up or down, making them a powerful tool for solving proportional problems.

Learn how to solve a ratio problem involving hockey and badminton players. Given a ratio of 10:7 and 70 hockey players, find the number of badminton players in the school. Step-by-step solution provided.

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