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Math Help - Problem Solving

  1. #1
    Member Mr Rayon's Avatar
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    Wink Problem Solving

    Okay, a mother is 7 times as old as her son. In five years time she will be 4 times her son's age. How old is the mother now?




    Please show any working out. All help is appreciated.
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by Mr Rayon View Post
    Okay, a mother is 7 times as old as her son. In five years time she will be 4 times her son's age. How old is the mother now?




    Please show any working out. All help is appreciated.
    Okay, lets use x to be the age of the son, and y to be the age of the mother.

    Then the first equation says: a mother is 7 times as old as her son so:
    y = 7x

    Pretty straight forward.

    And the second equation says: In five years time she will be 4 times her son's age.

    This one takes a little more thought. if she is y years old now, then she will be y+5 years old in 5 years. So the LHS (left hand side) becomes y+5. And at that time she will be 4 times as old as her son, so the RHS becomes 4x. However, her son must have also aged 5 years, so x needs to be replaced with (x+5) and thus 4x becomes 4(x+5)
    y+5 = 4(x+5)

    Now we have two equations, lets substitute the top equation into the bottom equation:

    y+5 = 4(x+5) becomes 7x+5 = 4(x+5)

    Now we can distribute the 4 on the RHS
    7x+5 = 4x+20

    subtract 4x and subtract 5

    3x = 15

    divide by 3

    x = 5

    So we know that the son is 5 years old now. Lets substitute this value back into either equation to get a value for y. I'll do the top one since it is a simpler equation:

    y=7x

    y=7*5

    y=35

    So the mother is 35 years old, and the son is 5 years old.

    To check our work, we can see that she is 7 times as old as he is, and that in 5 years she will be 40 and he will be 10, and at that time she will be 4 times as old as he is. So we know we did it correctly.
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  3. #3
    Member Mr Rayon's Avatar
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    Wow, thank you so much. I totally get it now, if only my math teacher were as good you.
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