Blue and Red Cards

The man buys a pack of 72 cards. When he trades these he will get 12 blue cards and 12 red cards. And from those extra red cards he can get two additional blue cards, a total of 14 blue cards, and 2 red cards.

Trading 6 red cards for a blue card & extra red card is essentially trading 5 red cards for a blue card. With a 72-card deck you can trade for 14 blue cards, with 2 reds left over. 72/5 = 14 & 2/5.

So think of it like this: There are 72 red cards and if you trade 6 reds, you get a blue card and a red card back. So, if you dived 72 by 6, you get 12. So that's 12 blue cards. However, for every 6 red cards, you got 1 blue, and 1 red card, so you still have 12 red cards. What's 12 divided by 6? 2. So that's 2 more blue cards. If you add them up, 12+2, you get a total of 14 blue cards. Hope this helps!

~ =^.^=

Ok so I said if I get a 're card back I'm really only giving 5 red for one blue so 72 ÷5=14.4 he can only get 14 cards. Y'all make it so difficult lol

$\frac{72}{6} + \frac{72}{6^2} = \frac{72}{6} + \frac{72}{36} = 12+2 = \boxed{14}$ .

72 red cards gives 72/6= 12 blue cards and 12 red cards so that 12 red cards gives 2 blue cards and 2 red cards so finally he will get 12+2= 14 blue cards and 2 red cards

red cards = r

blue cards = b

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while r>6....

6r = r+b

72 = 6r

r1 = 12

b = 12 also, but this doesn't matter in the context of the problem.

if r>6, the problem has to go through another iteration.

12 = 6r

r2 = 2

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since r !> 6, the problem can be solved now.

r1+r2 = rt

12+2 = 14

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Thus, 14 is the answer.

(Longwinded, I know. Sorry.)

When ever he is giving 6 cards.. He will get back one among that...so we can assume for 5 red cards he will get an blue card...so 72/5 =14 where he has two red cards remaining

You can get 1 blue and 1 free red card instead of 6 red cards. So, we can say that we can get 1 blue card for 5 red cards(6 red cards - 1 free card). Thus, we can get 14 blue cards(72÷5). 2 is the remainder in 72÷5 which means we have 2 red card also. So, finally we have 14 blue cards and 2 red cards.