# arithmetic

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THE TOTAL AGE OF GROUP OF PARENTS IS 342.A NEW PARENT AGED 48 JOINS THE GROUP AND THE AVERAGE RISES BY 1. WHAT IS THE ORIGINAL AVERAGE.

• arithmetic -

Please use lower-case letters. Using capital letters, or upper case, in computer language is considered impolite, much like shouting. Besides it is much more difficult to read and most of us will not ruin our eyes by trying to read them.

Sra

• arithmetic -

let there be n parents

The average age at first is 342/n
After adding 1 parent and 48 years, the new average is 390/(n+1)

342/n + 1 = 390/(n+1)
342(n+1) + n(n+1) = 390n
342n + 342 + n + n^2 - 390n = 0
n^2 - 47n + 342 = 0

342 = 2*171 = 2*3*57 = 2*3*3*19

(n-38)(n-9) = 0

so there were either

38 parents average 9 years old (not likely), or
9 parents average 38 years old

when a 48-year old joins, there are now 10 parents avg age 39

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