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 Cracking my head
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By: Strawberry (offline)  Tuesday, March 19 2013 @ 08:00 AM CDT (Read 790 times)  
Strawberry

V, N and J had 258 Pokemon cards altogether at first. Later, V lost 10 cards, N's cards were doubled and J gave away 1/4 of his cards. In the end, V had half as many cards as N, and the the total number of cards V and N had was twice as many as what J had. What was the difference in the number of cards between J and V at first.

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By: echeewh (offline)  Tuesday, March 19 2013 @ 08:42 PM CDT  
echeewh

hi Strawberry,

Following pls find my worked solution:

This is a <work backwards> type question using models.

<after>
V |-----|
N |-----|-----|

Given that the total number of cards V and N had was twice as many as what J had, we split the V, N model above where 1 part(p) = 2 units(u) as follows.

V |--|--|
N |--|--|--|--|
J |--|--|--| *** { If V + N = 6u, then J = 3u }


Apply <work backwards> next to derive the <before> models.

<process>
J: - (1/4)
N: x 2
V: - 10

Reverse these 3 processes and we have the following :

<before>
V |--|--|<10>
N |--|--|
J |--|--|--|--|

Total: 258

8u --> 258 - 10 = 248
1u --> 31

J - V (at first) = 4u - 2u - 10 = 2u - 10
2u - 10 --> (2 × 31) - 10 = 62 - 10 = 52

===========

Trust this helps

Do let me know again if this is different from your Answerkey or if there's further clarification.

Cheers,
Edward

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