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Math Help - Age problem

  1. #1
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    Age problem

    In the year 1988 , Q's age is 3 times of P's age . R is 25 years younger than Q . In 1995 , S's age is a quarter of P's age . In 2004 , S is 21 years old . How old is R when S was born ?

    In 1988 , Q=3P

    R=Q-25

    In 1995 ,

    S=\frac{1}{4}(P+7)

    In 2004 ,

    S=21 --- S will be 21-9 = 12 in 1995 .

     <br />
12=\frac{1}{4}(P+7) \rightarrow P=41<br />

    P is 41-7=34 years old in 1988 .

    Q=3(34)=102 years old . Hence , R=102-25 =77years old .

    In 1988 , S was 5 years old .

    SO when S was born , R=77-5=72 years old .

    It is wrong .. Where is my mistake ? Thanks
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    In 1988 , Q=3P
    R=Q-25

    In 1995 ,
    S=\frac{1}{4}(P+7)

    In 2004 ,
    S=21 --- S will be 21-9 = 12 in 1995 .

    12=\frac{1}{4}(P+7) \rightarrow P=41

    P is 41-7=34 years old in 1988.
    You shouldn't have subtracted 7. When you assigned variables, P was P's age in 1988. P+7 is P's age in 1995. P = 41.

    Q=3(34)=102 years old . Hence , R=102-25 =77years old .
    Q = 3(41) = 123. (123 years old!?!?)
    R = 123 - 25 = 98

    In 1988 , S was 5 years old .
    SO when S was born , R=77-5=72 years old .
    R = 98 - 5 = 93 years old.


    01
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  3. #3
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    Quote Originally Posted by yeongil View Post
    You shouldn't have subtracted 7. When you assigned variables, P was P's age in 1988. P+7 is P's age in 1995. P = 41.


    Q = 3(41) = 123. (123 years old!?!?)
    R = 123 - 25 = 98


    R = 98 - 5 = 93 years old.


    01

    Huh , but the choices are

    (a) 19
    (b) 21
    (c) 26
    (d) 30
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  4. #4
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    Quote Originally Posted by thereddevils View Post
    In the year 1988 , Q's age is 3 times of P's age . R is 25 years younger than Q . Mr F says: It's not clear whether P's present age or P's age in 1988 is meant.

    In 1995 , S's age is a quarter of P's age . Mr F says: Again, it's not clear whether P's present age or P's age in 1995 is meant.

    [snip]
    Assuming the latter interpretation in each case, post #2 gives the correct answer. Since this is not one of the choices, some other interpretation of P's age is probably being used by the book. To be honest, I don't see the point in working through each of those different possible interpretations.
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  5. #5
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    Hello, thereddevils!

    Is there a typo?
    The numbers don't seem to be reasonable.


    In 1988: Q's age was 3 times of P's age; R was 25 years younger than Q.

    In 1995: S's age is a quarter of P's age.

    In 2004: S is 21 years old.

    How old was R when S was born ?
    Let x = P's age in 1988.


    In 1988, we have:

    . . \begin{array}{c|c|c|c|}<br />
& P & Q & R \\ \hline \hline<br />
1988 & x & 3x & 3x-25 \\ \hline\end{array}



    In 1985 (7 years later), we have:

    . . \begin{array}{c|c|c|c|c|}<br />
& P & Q & R & S \\ \hline \hline<br />
1995 & x+7 & 3x+7 & 3x-18 & \frac{1}{4}(x+7) \\ \hline \end{array}



    In 2004 (9 years later), we have:

    . . \begin{array}{c|c|c|c|c|}<br />
& P & Q & R & S \\ \hline \hline<br />
2004 & x+16 & 3x+16 & 3x - 9 & \frac{1}{4}(x+7)+9 \\ \hline \end{array}

    At this time, S is 21: . \tfrac{1}{4}(x+7) + 9 \:=\:21

    . . \tfrac{1}{4}(x+7) \:=\:12 \quad\Rightarrow\quad x + 7 \:=\:48 \quad\Rightarrow\quad x \:=\:41


    Therefore, in 1988, P was 41 years old . . . and {\color{blue}Q} was 123 ??

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  6. #6
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    Quote Originally Posted by Soroban View Post
    Hello, thereddevils!

    Is there a typo?
    The numbers don't seem to be reasonable.

    Let x = P's age in 1988.


    In 1988, we have:

    \begin{array}{c|c|c|c|}<br />
& P & Q & R \\ \hline \hline<br />
1988 & x & 3x & 3x-25 \\ \hline\end{array}



    In 1985 (7 years later), we have:

    \begin{array}{c|c|c|c|c|}<br />
& P & Q & R & S \\ \hline \hline<br />
1995 & x+7 & 3x+7 & 3x-18 & \frac{1}{4}(x+7) \\ \hline \end{array}



    In 2004 (9 years later), we have:

    \begin{array}{c|c|c|c|c|}<br />
& P & Q & R & S \\ \hline \hline<br />
2004 & x+16 & 3x+16 & 3x - 9 & \frac{1}{4}(x+7)+9 \\ \hline \end{array}

    At this time, S is 21: . \tfrac{1}{4}(x+7) + 9 \:=\:21

    . . \tfrac{1}{4}(x+7) \:=\:12 \quad\Rightarrow\quad x + 7 \:=\:48 \quad\Rightarrow\quad x \:=\:41


    Therefore, in 1988, P was 41 years old . . . and {\color{blue}Q} was 123 ??

    Well , the question .. the numbers i mean don seem to be reasonable to me too . Anyways , thanks for the help . Now i know how to solve questionslike this .
    Last edited by mr fantastic; July 21st 2009 at 12:53 AM. Reason: Fixed quote (the latex was messed up)
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