Bobby had ³₄ as many cards as Billy. Billy had ⁴₇ as many cards as Sabrina. After Bobby and Sabrina gave 22 cards to Billy, Billy had thrice as many cards as Bobby. Sabrina then had the same number of cards as Billy.

1. What was the ratio of the number of cards Bobby had to the number of cards Sabrina had in the beginning? Answer in simplest form.
2. How many cards did Billy have in the end?

Bobby	Billy	Sabrina
3	4
	4	7
3	4	7

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

Ratio of the number of cards that Bobby had to the number of cards that Sabrina had in the beginning = 3 : 7

	Bobby	Billy	Sabrina	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 22	+ 44	- 22
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 Billy received from Bobby and Sabrina
= 2 x 22
= 44

Number of cards that Billy received from Bobby and Sabrina
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of cards that Ashley had in the end
= 6 u
= 6 x 11
= 66