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?

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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) About Me  (Show Source):
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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