Harry had ¹₂ as many beads as Lee. Lee had ²₃ as many beads as Tammy. After Harry and Tammy gave 18 beads to Lee, Lee had four times as many beads as Harry. Tammy then had the same number of beads as Lee.

1. What was the ratio of the number of beads Tammy had to the number of beads Harry had in the beginning? Answer in simplest form.
2. How many beads did Lee have in the end?

Harry	Lee	Tammy
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Tammy had to the number of beads that Harry had in the beginning = 3 : 1

	Harry	Lee	Tammy	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 18	+ 36	- 18
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 6 and 9 is 18.

Number of beads that Lee received from Harry and Tammy
= 2 x 18
= 36

Number of beads that Lee received from Harry and Tammy
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads that Ashley had in the end
= 8 u
= 8 x 9
= 72