Question : Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10% more stamps than Jennifer. How many stamps did Jennifer begin with ?
Correct Solution below:
- Initially Peter has $P$ stamps and Jennifer has $1.4P$
- Then; solving $P+45 = 1.1(1.4P-45)$ equation gives us P=175 and J=245.
I tried 2 solutions, both of my solutions gave me different result. I wish to understand the mistake i made in each of them. Most probably i have made mistake while creating the equation, but unable to find it as i feel my equation is right as per word problem.
1st Approach
- Initially Jennifer has $J$ stamps and Peter has $0.6J$ (because peter has 40% less stamps of Jennifer)
- Then; solving $0.60J+45=1.1(J-45)$ equation gives J=189 and P=113.4
$0.60J+45=1.1(J-45)$ // when peter has 45 more stamps = 10% more stamps of jennifer
$0.60J+45=1.1J-49.5$
$49.5+45=1.1J-0.60J$
$94.5=0.5J$
$J=189$ and $P=113.4$ after solving $0.6J$
2nd Approach - Initially Jennifer has $J$ stamps and Peter has $0.6J$ - Then; solving $J-45=0.9(0.6J+45)$ equation gives J=185.86... & P=111.52...
$J-45=0.9(0.6J+45)$ // when jennifer has 45 less stamps = 0.90% of peters stamp
$J-45=0.54J+40.5$
$J-0.54J=45+40.5$
$0.46J=85.5$ which gives J=185.86... & P=111.52...
The mistake is at the first line.
If Jennifer has $J$. We have $J= 1.4P$, that is $P=\frac1{1.4}J \approx 0.714J$. We do not have $P = 0.6J$.
When we say Jennifer has $40\%$ more stamps than Peter. View Peter having $100$ units of stamps while Jennifer has $140$ units. It is different from viewing Jennifer as having $100$ units and Peter having $60$ units.