The mean height of 45 students is 152cm. If the mean height of girls alone is 144cm and that of boys alone is 168cm. Find the number of boys and girls in the class
g = number of girls
b = number of boys
SG = Sum of height of all girls
SB = Sum of height of all boys
There are 45 studentss in the class.
g = 45 - b
The mean height of girls:
Sum of height of all girls / g = 144
SG / g = 144
SG = 144 ∙ g
SG = 144 ∙ ( 45 - b )
SG = 6480 - 144 b
The mean height of boys:
Sum of height of all boys / b = 168 cm
SB / b = 168
SB = 168 b
The mean height of 45 students is 152cm.
( SG + SB ) / 45 = 152
( 6480 - 144 b + 168 b ) / 45 = 152
6480 + 24 b = 45 ∙ 152
6480 + 24 b = 6840
24 b = 6840 - 6480
24 b = 360
b = 360 / 24
b = 15
g = 45 - b = 45 - 15 = 30
There are 30 girls and 15 boys in the class.
Let's assume the number of girls in the class is "g" and the number of boys is "b".
From the information given, we can determine the following:
1. The mean height of all students is 152cm.
2. The mean height of girls alone is 144cm.
3. The mean height of boys alone is 168cm.
To find the number of boys and girls in the class, we can set up the following equations:
1. Total height of all students = mean height * number of students
152cm * 45 = 6840cm
2. Total height of girls = mean height of girls * number of girls
144cm * g
3. Total height of boys = mean height of boys * number of boys
168cm * b
Since the total height of all the students is the sum of the total height of girls and boys, we can write the equation:
Total height of all students = Total height of girls + Total height of boys
6840cm = 144cm * g + 168cm * b
We also know that the total number of students is the sum of the number of girls and boys:
Total number of students = number of girls + number of boys
45 = g + b
Now we have a system of two equations:
1. 6840cm = 144cm * g + 168cm * b
2. 45 = g + b
We can solve this system of equations to find the values of g and b.
To find the number of boys and girls in the class, we can use the concept of algebraic equations based on mean values.
Let's assume the number of girls in the class is 'G' and the number of boys is 'B'.
1. We know that the mean height of all 45 students is 152cm. This means that the total height of all students is 152cm times 45 students, which can be written as:
Total height = 152 * 45
2. We also know that the mean height of all girls alone is 144cm. So, the total height of all girls is 144cm times the number of girls, which can be written as:
Total height of girls = 144 * G
3. Similarly, the mean height of all boys alone is 168cm. So, the total height of all boys is 168cm times the number of boys, which can be written as:
Total height of boys = 168 * B
Now, we can write an equation based on the total height of all students, girls, and boys:
Total height = Total height of girls + Total height of boys
Substituting the known values into the equation:
152 * 45 = 144 * G + 168 * B
Simplifying the equation:
6840 = 144G + 168B
Since there are only girls (G) and boys (B) in the class, the number of students is equal to the sum of girls and boys:
G + B = 45
Now we have a system of equations:
6840 = 144G + 168B
G + B = 45
We can solve this system of equations to find the number of girls (G) and boys (B) in the class.