Nick, Charlie and Howard have some cards. The ratios of their cards are as follows:

Nick : (Nick + Charlie + Howard) = 2 : 5
Charlie : (Nick + Howard) = 1 : 5

Howard has 56 cards more than Charlie. In the end, Howard gives away all he has to Charlie and Nick so that both Charlie and Nick end up with the same number of cards, how many cards has Charlie received from Howard?

Charlie	Howard	Nick	Total
3x6		2x6	5x6
1x5	5x5		6x5
5 u	13 u	12 u	30 u

The total number of cards is repeated.  Make the total number of cards the same.  LCM of 5 and 6 is 30.

Number of cards that Howard has more than Charlie
= 13 u - 5 u
= 8 u

8 u = 56

1 u = 56 ÷ 8 = 7

	Charlie	Howard	Nick
Before	5 u	13 u	12 u
Change	+ 10 u	- 13 u	+ 3 u
After	15 u	0 u	15 u

Number of cards that Charlie has received from Howard
= 15 u - 5 u 
= 10 u
= 10 x 7
= 70

Answer(s): 70