Question

14. The average height of a group of girls was 155 cm.When 15 boys joined the group, the average height became 158 cm.Given that the average height of the 15 boys was 165 cm, find the number of girls inthe group

Answer 1

The average height of the 15 boys was 165 cm, so the total height of the 15 boys is:

H(boys) = 15 * 165 = 2475 cm

Let's call the number of girls 'n'.

So, if the average height of the girls is 155 cm, the total height of the girls is:

H(girls) = n * 155 = 155n cm

Then, when we have boys and girls together, the total number of people is '15 + n', and the average is 158 cm, so the total height is:

H(boys and girls) = (15 + n) * 158 = 2370 + 158n

Now, summing the total height of boys and the total height of girls, we have the total height:

H(boys and girls) = H(boys) + H(girls)

2370 + 158n = 2475 + 155n

158n - 155n = 2475 - 2370

3n = 105

n = 35

So we have that the number of girls in the group is 35.