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Stamps word problem

  1. Oct 21, 2012 #1
    I got the word problem off the internet, just for a bit of practice, and get slightly lost towards the end. It tells me becky had 216 stamps, the thing is I am not to sure how to set up the equation I will show my working below.


    Ada, Becky and Cathy had some stamps. Cathy had 20%more stamps than Ada. Cathy had 75% as many stamps as Becky. Becky gave 45 stamps to Ada and Cathy in the ratio of 4:1 so that all three girls will have the same number of stamps.

    a) How many stamps did Becky have at first?

    1. [itex]C=A*120\%[/itex] [itex]C=B*75\%[/itex]

    2. ratio [itex]\frac{45}{5}=9[/itex] [itex]9*4=36[/itex][itex]9*1=9[/itex]

    3. [itex]B-45=C+9=A+36[/itex]

    This is the point of confusion, I am not quite sure how to solve for B. I know I should some how sub 1 into 3 to make the equation, but not to sure how? could someone point me in the right direction, to how to solve this.

    I did convert the percentages to fraction: [itex]\frac{6}{5}[/itex] and [itex]\frac{3}{4}[/itex] but still did not help.

    Would really apprecaite the guidence
     
  2. jcsd
  3. Oct 21, 2012 #2
    From this point, all you need to do is substitute [itex] .75B [/itex] for [itex]C[/itex] and solve for [itex]B[/itex], forgetting about [itex]A[/itex], though you can check to make sure you got it right by solving for all of the final stamp counts.
     
  4. Oct 21, 2012 #3
    If I solve for [itex] B [/itex] I get [itex] 207 [/itex], I should be getting [itex]216[/itex]

    Here is how I did it, I personally cant see where I am going wrong, but obviously I am somewhere: [itex]B-45=\frac{3}{4}B+9[/itex] [itex]\rightarrow[/itex] [itex]4(B-45)=3(B+9)[/itex] [itex]\rightarrow[/itex] [itex]4B-180=3B+27[/itex] [itex]\rightarrow[/itex] [itex]B=207[/itex]
     
  5. Oct 21, 2012 #4
    [itex] B - 45 = .75B + 9 [/itex]

    [itex] .25B = 54 \Rightarrow B = 216 [/itex]

    Your problem was that you solved it as though it was:

    [itex] B - 45 = \frac{3}{4}(B+9) [/itex]

    and [itex] \frac{3}{4}(B+9) \neq \frac{3}{4} B + 9 [/itex]
     
  6. Oct 21, 2012 #5
    Got it, thanks for that fella; been bugging me all day.
     
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