SOLUTION: 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 tr

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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?
Found 4 solutions by Boreal, htmentor, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Ron bought r postcards
Matt bought some other number of postcards, m.
Half of Ron's postcards, or r/2, were given to Matt, who gave 9 to Ron.
Ron now has (r/2)+9. Matt now has m-9+(r/2)
Each has 21
so Ron has (r/2)+9=21
subtract 9 from each side
(r/2)=12
r=24, multiplying both sides by 2, removing the denominator.
Matt has 21=m-9+(r/2)
21=m-9+12, the 12 from above
21=m+3
m=18 postcards for him
24 and 18
Ron gave 12 to Matt, leaving him with 12, but he got 9 more, giving him 21
Matt had 18, giving Ron 9 leaving him with 9, but he got 12 more, giving him 21.
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
Let R = Ron's postcards before the trade
Let M = Matt's postcards before the trade
After the trade, Ron has R/2 + 9 since he traded half and received 9 from Matt
After the trade, Matt has M - 9 + R/2 since he gave away 9 and received half of Ron's
Both have 21 after the trade. In equation form this is:
R/2 + 9 = 21
M - 9 + R/2 = 21
The first equation gives R = 24
Solving for M in the second equation we get:
M - 9 + 12 = 21
This gives M = 18
Ron has 24, Matt has 18
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~ 


Ron gave half of his postcards to Matt and obtained 9 postcards from Matt.
As a result, Ron has 21 postcards.


    It means that before obtaining 9 postcards from Matt, Ron had 21-9 = 12 postcards,
    and it is HALF of that he had originally.

    Hence, originally Ron had 2*12 = 24 postcards.




Matt obtained half of Ron's postcards, i.e. 24/2 = 12 postcards, but gave to Ron 9 his postcards.


    Thus Matt increases the number of his postcards by (12-9) = 3 postcards, having finally 21 postcards.

    Hence, Matt possessed 21-3 = 18 postcards originally.


ANSWER.  Ron had originally 24 postcards.  

         Matt had originally 18 postcards.


----------------

Can your 5-grader understand it ?



Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

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?
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  of what he originally had, then before trading  to Matt, he had TWICE the amount that he had after trading

 of his original number of postcards. Therefore, before trading  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  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.  

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