Solve Word Problem: Becky Had 216 Stamps

[Taylor_1989]

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. $C=A*120\%$ $C=B*75\%$

2. ratio $\frac{45}{5}=9$ $9*4=36$$9*1=9$

3. $B-45=C+9=A+36$

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: $\frac{6}{5}$ and $\frac{3}{4}$ but still did not help.

Would really apprecaite the guidence

 

[bossman27]

From this point, all you need to do is substitute $.75B$ for $C$ and solve for $B$, forgetting about $A$, though you can check to make sure you got it right by solving for all of the final stamp counts.

 

[Taylor_1989]

From this point, all you need to do is substitute $.75B$ for $C$ and solve for $B$, forgetting about $A$, though you can check to make sure you got it right by solving for all of the final stamp counts.

If I solve for $B$ I get $207$, I should be getting $216$

Here is how I did it, I personally can't see where I am going wrong, but obviously I am somewhere: $B-45=\frac{3}{4}B+9$ $\rightarrow$ $4(B-45)=3(B+9)$ $\rightarrow$ $4B-180=3B+27$ $\rightarrow$ $B=207$

 

[bossman27]

$B - 45 = .75B + 9$

$.25B = 54 \Rightarrow B = 216$

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

$B - 45 = \frac{3}{4}(B+9)$

and $\frac{3}{4}(B+9) \neq \frac{3}{4} B + 9$

 

[Taylor_1989]

Got it, thanks for that fella; been bugging me all day.