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Height problem

  1. Jan 2, 2016 #1
    1. The problem statement, all variables and given/known data

    Emily's brother, Jack, is now 105cm tall, having grown by one sixth of his height a year ago. How tall was Jack one year ago?

    2. Relevant equations

    Now my teacher told me to do this:

    x = 105 - (105/7)
    x = 105 - 15
    x = 90 cm

    3. The attempt at a solution

    So 90cm is the answer. But can someone explain to me very simply why we divided by 7 the 105 as the question says that Jack grew by one sixth and not by one seventh? Many thanks.
     
  2. jcsd
  3. Jan 2, 2016 #2

    SammyS

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    Maybe looking at it a different first would help.

    Let x be Jack's height one year ago.

    Add x plus x/6 to get 105.

    Solve for x:
    ##\displaystyle \ x+\frac{x}{6}=105 \ ##
     
  4. Jan 2, 2016 #3
    Ahh,

    So 7x = 105
    x = 15
     
  5. Jan 2, 2016 #4

    SammyS

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    Actually it's more like:
    ##\displaystyle \ 7\left(\frac{x}{6}\right)=105 \ ,##​
    so that
    ##\displaystyle \ \frac{x}{6}=\frac{105}7 \ ,##​
    etc.
     
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