SOLUTION: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is?

Question 1089341: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the average age in months of the class before the change was made. Then

is the total of all the boys' ages in months. After the 18-year-old boy leaves the class and is replaced by the new boy whose age in months we will represent with

, the average is reduced by 2 months, so the total of all the boys' ages in months for the new configuration of the class is

. Since there are 216 months in 18 years, we can write:

Which simplifies to:

Solve for

to find the new boy's age in months. Divide that result using integer division to find the new boy's age in years and months (quotient is years, remainder is months)

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
The average age of 30 boys in a class is 15 years. One boy aged 20 years, left the class, (answered by Theo)

The average age of a group of 20 boys is increased by one year when 5 of them whose... (answered by god2012)

The average age of a group went up by 2 years when a man aged 34 years was replaced by an (answered by ankor@dixie-net.com)

The average age of 8 men is decreased by 2 years, when two of them, whose ages are 22 and (answered by scott8148)

Please help! the average age of 8 men is decreased by 2 years when two of them whose... (answered by MathLover1)

The average age of the boys in a class of 20 boys is 15.6 years. What will be the... (answered by god2012)

the average age of 8 men is increased by 2 years when 2 of them whose ages are 21 years... (answered by Theo)

The average age of 8 men is increased by 2 years when two of them whose ages are 21 years (answered by robertb)

The average age of 25 boys in a class is 12 years. If three boys aged 13, 14 and 15 and... (answered by Fombitz)