Luis had ¹₂ as many beads as Lee. Lee had ²₃ as many beads as Penelope. After Luis and Penelope gave 26 beads to Lee, Lee had four times as many beads as Luis. Penelope then had the same number of beads as Lee.

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

Luis	Lee	Penelope
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Penelope had to the number of beads that Luis had in the beginning = 3 : 1

	Luis	Lee	Penelope	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 26	+ 52	- 26
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 Luis and Penelope
= 2 x 26
= 52

Number of beads that Lee received from Luis and Penelope
= 2 x 1 u
= 2 u

2 u = 26

1 u = 26 ÷ 2 = 13

Number of beads that Ashley had in the end
= 8 u
= 8 x 13
= 104