Luke had ¹₂ as many stickers as Howard. Howard had ²₃ as many stickers as Betty. After Luke and Betty gave 4 stickers to Howard, Howard had four times as many stickers as Luke. Betty then had the same number of stickers as Howard.

1. What was the ratio of the number of stickers Luke had to the number of stickers Betty had in the beginning? Answer in simplest form.
2. How many stickers did Howard have in the end?

Luke	Howard	Betty
1	2
	2	3
1	2	3

(a)
The number of stickers that Howard is repeated.  

Ratio of the number of stickers that Luke had to the number of stickers that Betty had in the beginning = 1 : 3

	Luke	Howard	Betty	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 4	+ 8	- 4
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of stickers that Howard received from Luke and Betty
= 2 x 4
= 8

Number of stickers that Howard received from Luke and Betty
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of stickers that Ashley had in the end
= 8 u
= 8 x 2
= 16