Nick had ³₄ as many cards as Harry. Harry had ⁴₇ as many cards as Gem. After Nick and Gem gave 4 cards to Harry, Harry had thrice as many cards as Nick. Gem then had the same number of cards as Harry.

1. What was the ratio of the number of cards Nick had to the number of cards Gem had in the beginning? Answer in simplest form.
2. How many cards did Harry have in the end?

Nick	Harry	Gem
3	4
	4	7
3	4	7

(a)
The number of cards that Harry is repeated.  

Ratio of the number of cards that Nick had to the number of cards that Gem had in the beginning = 3 : 7

	Nick	Harry	Gem	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 4	+ 8	- 4
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of cards at first and in the end remains unchanged. Make the total number of cards the same. LCM of 14 and 7 is 14.

Number of cards that Harry received from Nick and Gem
= 2 x 4
= 8

Number of cards that Harry received from Nick and Gem
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of cards that Ashley had in the end
= 6 u
= 6 x 2
= 12