Question

. The sum of the ages of x boys in a class is 84 years. When a new boy aged 8 years, 1 month joins the class, the average age is increased by 1 month

Answer 1

The number of boys, x = 12

Explanation:

Given that the sum of the ages of the boys in a class = 84 years

The number of boys = x

A new boy aged 8 years 1 month is added and the average age increases by 1 month

We have

Average age = 84/x = y

Age of new boy = 8 years 1 month =
`8(1)/(12) \ year`

New average = y + 1/12 =
`(8(1)/(12)+84) /(x + 1)` which gives;

84/x + 1/12 =
`(8(1)/(12) + 84) /(x + 1)`

`(x +1008)/(12 \cdot x) = (1105)/(12 \cdot x+ 12)`

(x + 1008)×(12·x + 12) = 1105× 12·x

12·x² -1152·x + 12096 = 0

x² -96·x + 1008 = 0

(x - 84)×(x - 12) = 0

Therefore, x = 12 or 84,

The number of boys are 12 or 84

For there to bee 84 boys, their average age would be one year each

Given that they are boys not babies, then there are only 12 boys.