Ben had ³₄ as many beads as Pierre. Pierre had ⁴₇ as many beads as Tina. After Ben and Tina gave 18 beads to Pierre, Pierre had thrice as many beads as Ben. Tina then had the same number of beads as Pierre.

1. What was the ratio of the number of beads Tina had to the number of beads Ben had in the beginning? Answer in simplest form.
2. How many beads did Pierre have in the end?

Ben	Pierre	Tina
3	4
	4	7
3	4	7

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

Ratio of the number of beads that Tina had to the number of beads that Ben had in the beginning = 7 : 3

	Ben	Pierre	Tina	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 18	+ 36	- 18
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 Pierre received from Ben and Tina
= 2 x 18
= 36

Number of beads that Pierre received from Ben and Tina
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads that Ashley had in the end
= 6 u
= 6 x 9
= 54