John had ¹₂ as many stamps as Luis. Luis had ²₃ as many stamps as Jean. After John and Jean gave 20 stamps to Luis, Luis had four times as many stamps as John. Jean then had the same number of stamps as Luis.

1. What was the ratio of the number of stamps Jean had to the number of stamps John had in the beginning? Answer in simplest form.
2. How many stamps did Luis have in the end?

John	Luis	Jean
1	2
	2	3
1	2	3

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

Ratio of the number of stamps that Jean had to the number of stamps that John had in the beginning = 3 : 1

	John	Luis	Jean	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 20	+ 40	- 20
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of stamps that Luis received from John and Jean
= 2 x 20
= 40

Number of stamps that Luis received from John and Jean
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of stamps that Ashley had in the end
= 8 u
= 8 x 10
= 80