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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 - ,

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  • 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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