Xavier had ³₄ as many cards as Japheth. Japheth had ⁴₇ as many cards as Opal. After Xavier and Opal gave 14 cards to Japheth, Japheth had thrice as many cards as Xavier. Opal then had the same number of cards as Japheth.

1. What was the ratio of the number of cards Xavier had to the number of cards Opal had in the beginning? Answer in simplest form.
2. How many cards did Japheth have in the end?

Xavier	Japheth	Opal
3	4
	4	7
3	4	7

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

Ratio of the number of cards that Xavier had to the number of cards that Opal had in the beginning = 3 : 7

	Xavier	Japheth	Opal	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 14	+ 28	- 14
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 Japheth received from Xavier and Opal
= 2 x 14
= 28

Number of cards that Japheth received from Xavier and Opal
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of cards that Ashley had in the end
= 6 u
= 6 x 7
= 42