Billy had ³₄ as many stamps as Bobby. Bobby had ⁴₇ as many stamps as Lucy. After Billy and Lucy gave 28 stamps to Bobby, Bobby had thrice as many stamps as Billy. Lucy then had the same number of stamps as Bobby.

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

Billy	Bobby	Lucy
3	4
	4	7
3	4	7

(a)
The number of stamps that Bobby is repeated.  

Ratio of the number of stamps that Lucy had to the number of stamps that Billy had in the beginning = 7 : 3

	Billy	Bobby	Lucy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

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

Number of stamps that Bobby received from Billy and Lucy
= 2 x 28
= 56

Number of stamps that Bobby received from Billy and Lucy
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of stamps that Ashley had in the end
= 6 u
= 6 x 14
= 84