https://file.aiquickdraw.com/mathbot/file/17264046118761sihvwq0.jpg

The problem can be solved by following these steps:

1. **Initial Mean Calculation**:
   The mean height of the team of 11 players is 1.71 m. Thus, the total height of the team initially is:
   
   \[
   \text{Total initial height} = 1.71 \times 11 = 18.81 \text{ meters}
   \]

2. **Substitution**:
   A central defender who is 1.95 m tall is substituted. So, after the substitution, the new total height of the team becomes:
   
   \[
   \text{New total height} = \text{Initial total height} - 1.95 + \text{Height of substitute}
   \]

   The new mean height of the team is 1.68 m. Therefore, the new total height of the team is:
   
   \[
   \text{New total height} = 1.68 \times 11 = 18.48 \text{ meters}
   \]

3. **Find the Height of the Substitute**:
   From the above equation:
   
   \[
   18.48 = 18.81 - 1.95 + \text{Height of substitute}
   \]
   
   Solving for the height of the substitute:
   
   \[
   \text{Height of substitute} = 18.48 - 18.81 + 1.95 = 1.62 \text{ meters}
   \]

Thus, the height of the substitute is **1.62 meters**.

---

Would you like any further details or explanations? Here are some related questions to deepen your understanding:

1. How is the mean height of a group calculated?
2. What would the mean height be if the substitute were 1.70 meters tall instead?
3. How does the substitution affect the total height of the team?
4. Can you generalize this method to find the height of a substitute player given any initial conditions?
5. How would the problem change if more than one player was substituted?

**Tip**: To solve problems with averages, always focus on how changes affect the total sum of values!

The mean height of a football team of 11 players is 1.71m. A central defender, who is 1.95m tall, is substituted with a smaller, more agile player. The mean height of the team is now reduced to 1.68m. How tall is the substitute?

Learn how to calculate the height of a substitute football player when the mean height of the team decreases. This problem involves algebra and average calculation, perfect for students in Grades 7-9. Explore key concepts such as the mean formula and solving simple equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation