Tommy had ¹₂ as many pens as Harry. Harry had ²₃ as many pens as Risa. After Tommy and Risa gave 10 pens to Harry, Harry had four times as many pens as Tommy. Risa then had the same number of pens as Harry.

1. What was the ratio of the number of pens Tommy had to the number of pens Risa had in the beginning? Answer in simplest form.
2. How many pens did Harry have in the end?

Tommy	Harry	Risa
1	2
	2	3
1	2	3

(a)
The number of pens that Harry is repeated.  

Ratio of the number of pens that Tommy had to the number of pens that Risa had in the beginning = 1 : 3

	Tommy	Harry	Risa	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 10	+ 20	- 10
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of pens that Harry received from Tommy and Risa
= 2 x 10
= 20

Number of pens that Harry received from Tommy and Risa
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of pens that Ashley had in the end
= 8 u
= 8 x 5
= 40