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# Marty has a coin collection, which consists of only New World and Old

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
Marty has a coin collection, which consists of only New World and Old  [#permalink]

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16 Aug 2017, 01:59
1
1
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Difficulty:

15% (low)

Question Stats:

83% (02:13) correct 17% (02:19) wrong based on 70 sessions

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Marty has a coin collection, which consists of only New World and Old World coins, in a ratio of 3:1. Marty’s friend Kyle swaps 28 of his Old World Coins for 28 of Martin’s New World coins. If Marty now has as many Old World coins as he does New World coins, how many coins did Marty originally have in his collection?

(A) 28

(B) 84

(C) 112

(D) 130

(E) 390

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Re: Marty has a coin collection, which consists of only New World and Old  [#permalink]

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16 Aug 2017, 02:12
1
3x-28/x+28=1; 2x=56; x=28; 4x=112
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Re: Marty has a coin collection, which consists of only New World and Old  [#permalink]

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16 Aug 2017, 04:39
2
$$\frac{Nw}{Ow}$$=3=> Nw= 3Ow

After the swap
Nw-28= Ow+28
=>3 Ow-28= Ow+28
=>2Ow= 56
=>Ow= 28
Nw=3ow= 28*3= 84

Total coins originally = 84+28=112

Ans- C
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Joined: 30 May 2017
Posts: 7
Marty has a coin collection, which consists of only New World and Old  [#permalink]

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16 Aug 2017, 05:47
Old Ratio (New Coins:Old Coins) : 3:1
Total Coins = 3n + n = 4n

New Ratio: 1:1
New Arrange: (3n-28 / n+28) = (1/1)

Cross Multiply:
3n-28=n+28
2n = 56
n = 28

So, 4n = 112
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Re: Marty has a coin collection, which consists of only New World and Old  [#permalink]

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08 Dec 2019, 15:39
Hi All,

We're told that Marty has a coin collection, which consists of only New World and Old World coins, in a ratio of 3:1. Marty's friend Kyle swaps 28 of his Old World Coins for 28 Marty's New World Coins and then Marty now has as many Old World Coins as he does New World Coins. We're asked for the total number of coins that Marty originally had in his collection. Since we're dealing with ratios, this question can be solved in a number of different ways, including by TESTing THE ANSWERS.

To start, since the original ratio of New to Old coins was 3:1, this means that Marty's TOTAL COINS has to be a MULTIPLE of 4. Depending on how quickly you can do division, you'll notice that neither Answer D nor Answer E is a multiple of 4, so both of those answers can be eliminated. Let's TEST Answer B first....

IF... Marty started off with 84 coins, with a ratio of 3:1, then he had 63 New coins and 21 Old coins
by 'swapping' 28 New coins for 28 Old coins, Marty would then have 35 New coins and 49 Old coins
This is NOT a match for what we were told though (Marty is supposed to have the SAME number of each). Since we're going to swap 28 coins no matter what, we need Marty to have MORE New coins at the start...

IF... Marty started off with 112 coins, with a ratio of 3:1, then he had 84 New coins and 28 Old coins
by 'swapping' 28 New coins for 28 Old coins, Marty would then have 56 New coins and 56 Old coins
Here, Marty has the SAME number of New and Old coins, so this MUST be the answer!

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Rich
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Re: Marty has a coin collection, which consists of only New World and Old   [#permalink] 08 Dec 2019, 15:39
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