Question 1128070

Would appreciate a simple solution that a 5th grader can understand. Thanks in advance!

Ron and Matt both bought postcards during their trip to New Zealand. At the end of the trip, they decided to trade. Ron traded half of his postcards for 9 of Matt’s postcards. After that trade, each of them has 21 postcards. How many postcards did Ron have before the trade? How many postcards did Matt have before the trade?
<pre>The BEST and SIMPLEST 5th grade solution is to GO BACKWARDS, as follows:
Ron ended up with 21 postcards after receiving 9 of Matt's, so let's SUBTRACT the 9 to get 12 (21 - 9). 
Since Ron traded {{{1/2}}} of what he originally had, then before trading {{{1/2}}} to Matt, he had TWICE the amount that he had after trading
{{{1/2}}} of his original number of postcards. Therefore, before trading {{{1/2}}} to Matt, ORIGINAL number Ron had was: 2 * 12, or 24 postcards. 

Now, working backwards again: since Matt ended up with 21 postcards, if he should ADD back the 9 he gave to Ron, he'd end up with 30, 
and since Ron had given him {{{1/2}}} of his 24, or 12 postcards, we then SUBTRACT that 12 from the 30 that he now has and Matt ends up
with the ORIGINAL number of cards that he had which was 30 - 12, or 18.