Math Problem Statement

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

Solution

Let the number of girls in the class be gg, and the number of boys be bb. 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:

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

152×45=6840 cm152 \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=45g + b = 45
  2. 144g+168b=6840144g + 168b = 6840

Step 1: Solve equation (1) for bb:

b=45gb = 45 - g

Step 2: Substitute b=45gb = 45 - g into equation (2):

144g+168(45g)=6840144g + 168(45 - g) = 6840

Simplify: 144g+168×45168g=6840144g + 168 \times 45 - 168g = 6840 144g+7560168g=6840144g + 7560 - 168g = 6840 24g+7560=6840-24g + 7560 = 6840 24g=68407560-24g = 6840 - 7560 24g=720-24g = -720 g=72024=30g = \frac{-720}{-24} = 30

Step 3: Find bb:

b=45g=4530=15b = 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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Averages
Linear Equations

Formulas

Total height = Average height × Number of individuals
System of linear equations: g + b = 45, 144g + 168b = 6840

Theorems

Basic concept of averages
Solving systems of linear equations

Suitable Grade Level

Grades 8-10