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Math Help - Age Comparison Challenge

  1. #1
    Newbie Dried Monkey's Avatar
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    Age Comparison Challenge

    Hey, everyone. I have a problem for you to solve. I tried but don't know how to complete it. Here is the problem:

    "My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son, and I are 140 years. Can you tell me my age in years?"

    So that's what the problem said. If there are any answers, I'll gladly accept them. Thanks in advance!
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  2. #2
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    Hello, Dried Monkey!

    My grandson is about as many days as my son is weeks,
    and my grandson is as many months as I am in years.
    My grandson, my son, and I total 140 years.
    Can you tell me my age in years?

    Let: . \begin{array}{ccc}G &=& \text{Grandson's age in years} \\ S &=& \text{Son's age in years} \\ M &= & \text{My age in years} \end{array}


    Let's take each sentence separately.

    "My grandson is about as many days as my son is weeks."
    My son's age in days is seven times my grandson's age in days.
    That is, my son is seven times older than my grandson: . S \:=\:7G

    "And my grandson is as many months as I am in years."
    My grandson is G years old; that is, he is 12G months old.
    Hence, we have: . 12G \:=\:M

    "My grandson, my son, and I total 140 years": . G + S + M \:=\:140


    We have a system of equations: . \begin{array}{cccc} 7G - S &=& 0 & [1] \\ 12G - M &=& 0 & [2] \\ G + S + M &=&140 & [3] \end{array}

    \begin{array}{cccc}\text{Add [2] and [3]:} & 13G + S &=& 140 \\ \text{Add [1]:} & 7G - S &=& 0 \end{array}

    And we have: . 20G \:=\:140\quad\Rightarrow\quad G \:=\:7

    Substitute into [1]: . 7(7) - S \:=\:0 \quad\Rightarrow\quad S \:=\:49

    Substitute into [2]: . 12(7) - M \:=\:0 \quad\Rightarrow\quad M \:=\:84


    Therefore, my grandson is 7, my son is 49, and I am 84.

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  3. #3
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    Quote Originally Posted by Dried Monkey View Post
    Hey, everyone. I have a problem for you to solve. I tried but don't know how to complete it. Here is the problem:

    "My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son, and I are 140 years. Can you tell me my age in years?"

    So that's what the problem said. If there are any answers, I'll gladly accept them. Thanks in advance!
    Since the number of days in a month varies, you have to round a bit.

    X (days) = Y (weeks) => X = Y.

    X/30 (months) = Z (years) => X = 30 Z.

    \frac{X}{364} + \frac{Y}{52} + Z = 140.

    I get Z = 84 years.
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