Question

4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.​

Answer 1

8

Explanation:

The definition of an average can be used with the given values to write an equation for the number of boys.

Setup

The average is the total divided by the number. If there were n original boys, the total was T, where ...

T/n = 145 ⇒ T = 145n

Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...

(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320

Equating the values of T, we have ...

T = 145n = 148(n +2) -320

Solution

Solving for n, we find ...

0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify

0 = n -8 . . . . . . . . . . . divide by 3

8 = n . . . . . . . . . . . add 8

The number of boys in the group at first was 8.