THe average height of 45 pupils is 152 cm. if the average height of girls 

alone in 144cm, and that of boys alone is 168cm, find the number of boys and 

girls in the class 

Let the number of girls in the class be \( g \), and the number of boys be \( b \). We know the total number of pupils is 45, so:

\[
g + b = 45 \tag{1}
\]

Next, we're given the following average heights:

- The average height of the entire class is 152 cm.
- The average height of the girls is 144 cm.
- The average height of the boys is 168 cm.

Using the formula for average:

\[
\text{Total height of girls} = 144g
\]
\[
\text{Total height of boys} = 168b
\]

The total height of all pupils is the sum of the total height of girls and boys. Since the average height of all 45 pupils is 152 cm, the total height of all pupils is:

\[
152 \times 45 = 6840 \text{ cm}
\]

Thus, we have the equation:

\[
144g + 168b = 6840 \tag{2}
\]

Now, we solve the system of equations:

1. \( g + b = 45 \)
2. \( 144g + 168b = 6840 \)

### Step 1: Solve equation (1) for \( b \):
\[
b = 45 - g
\]

### Step 2: Substitute \( b = 45 - g \) into equation (2):
\[
144g + 168(45 - g) = 6840
\]

Simplify:
\[
144g + 168 \times 45 - 168g = 6840
\]
\[
144g + 7560 - 168g = 6840
\]
\[
-24g + 7560 = 6840
\]
\[
-24g = 6840 - 7560
\]
\[
-24g = -720
\]
\[
g = \frac{-720}{-24} = 30
\]

### Step 3: Find \( b \):
\[
b = 45 - g = 45 - 30 = 15
\]

Thus, there are **30 girls** and **15 boys** in the class.

---

Would you like any further details on this? 

Here are 5 related questions to extend your understanding:
1. What is the formula for calculating the average in general?
2. How would the solution change if the average height of the boys was different?
3. Can you find the total height of the boys and girls separately?
4. How can we verify if the solution is correct by substituting the values back into the equation?
5. How would you solve it if you were given the number of boys and asked to find the total average?

**Tip:** Always double-check units when solving word problems to avoid confusion, especially when dealing with averages.

The average height of 45 pupils is 152 cm. If the average height of girls alone is 144 cm, and that of boys alone is 168 cm, find the number of boys and girls in the class.

This problem explores how to find the number of boys and girls in a class of 45 students based on their average heights. Using algebra and systems of linear equations, students will solve for the number of boys and girls. Suitable for Grades 8-10.

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