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I need a simple solution that a 5th grader can understand.Would appreciate your help! 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?

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    $\begingroup$ Please share how you would solve the problem. Also, explain your student's background to make it possible for users of this site to write suitable answers. $\endgroup$ – N. F. Taussig Nov 5 '18 at 19:40
  • $\begingroup$ There is no explanation that a fifth grader can understand unless that fifth grader has a real knack for mathematics. $\endgroup$ – John Douma Nov 5 '18 at 19:46
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Let $x$ stand for the amount of postcards that Ron had before trading, and let $y$ stand for the amount of postcards that Matt had before trading. So, to find $x$ and $y$ we can form simple equations from the information given.

Now, if Ron had traded in half of his postcards, that means he’s got the other half left, that is, $\frac{x}{2}$, but then he got 9 in exchange from Matt, i.e. $\frac{x}{2} + 9$. Therefore $$\frac{x}{2} + 9 = 21 \implies \frac{x}{2} = 21 - 9 = 12 \\ \implies x = 12 * 2 = 24 $$

So Ron had 24 cards.

Now remember that Matt had $y$ cards before trading. We know he traded 9 of them in, which leaves us with $y-9$, but then got half of Ron’s cards in return, 12 as we know from our previous calculation. Therefore $$ 21 = y - 9 + 12 = y + 3 \\ y + 3 = 21 \implies y = 21 - 3 = 18 $$

So Matt had 18 cards.

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