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Math Help - figuring out the age

  1. #1
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    figuring out the age

    Maria is 6 times as old as Tina. In 20 years, Maria will be only twice as old as Tina. How old is Maria now?
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Judi
    Maria is 6 times as old as Tina. In 20 years, Maria will be only twice as old as Tina. How old is Maria now?
    I find the easiest way to do a problem is to write everything mathematically.

    first, define your variables...
    M=\text{Maria}
    T=\text{Tina}

    Next, write out what you know.

    Right now Maria is 6 times as old as Tina, therefore... M=6T

    In 20 years Maria will only be twice as old as Tina, therefore... M+20=2(T+20)

    Now we solve both equations for T

    M=6T\quad\rightarrow\quad \frac{M}{6}=T

    M+20=2(T+20)\quad\rightarrow\quad M+20= 2T+40\quad\rightarrow\quad M+20- 40=2T\quad\rightarrow\quad \frac{M-20}{2}=T

    Now we combine the two equations...

    \frac{M}{6}=\frac{M-20}{2} multiply by 6

    M=\frac{6(M-20)}{2} extend...

    M=\frac{3\cdot\not2(M-20)}{\not2} multiply by 3

    M=3M-60 subtract 3M from both sides...

    M-3M=-60\quad\rightarrow\quad-2M=-60\quad\rightarrow\quad \boxed{M=30}

    Voila!
    Last edited by Quick; July 6th 2006 at 01:45 PM. Reason: making mine look less like Soroban's way of posting
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  3. #3
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    Thank you,
    Judi
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  4. #4
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    Hello, Judi!

    Here's another approach . . . with one variable.


    Maria is 6 times as old as Tina.
    In 20 years, Maria will be only twice as old as Tina.
    How old is Maria now?

    Let x = Tina's age.

    Since Maria's age is 6 times Tina's age,
    . . then 6x = Maria's age.

    In 20 years, they will both be 20 years older.
    . . Tina will be x + 20 years old.
    . . Maria will be 6x + 20 years old.

    In the future, Maria's age is twice Tina's age.
    . . . . . . . . . . . . . . \downarrow\qquad\;\downarrow\quad\downarrow\qquad \,\downarrow
    . . . . . . . . . . . . 6x + 20 \;\;=\;\;2\cdot (x + 20)

    And there is your equation . . . go for it!

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  5. #5
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    You guys are awesome!!!
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