Fabian had ³₄ as many beads as John. John had ⁴₇ as many beads as Julie. After Fabian and Julie gave 28 beads to John, John had thrice as many beads as Fabian. Julie then had the same number of beads as John.

1. What was the ratio of the number of beads Fabian had to the number of beads Julie had in the beginning? Answer in simplest form.
2. How many beads did John have in the end?

Fabian	John	Julie
3	4
	4	7
3	4	7

(a)
The number of beads that John is repeated.  

Ratio of the number of beads that Fabian had to the number of beads that Julie had in the beginning = 3 : 7

	Fabian	John	Julie	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 beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 14 and 7 is 14.

Number of beads that John received from Fabian and Julie
= 2 x 28
= 56

Number of beads that John received from Fabian and Julie
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

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