Henry, Ryan and Japheth had a total of 58 erasers. The ratio of Ryan's erasers to Japheth's erasers was 4 : 5 at first. Henry and Ryan each gave away ¹₂ of their erasers. Given that the three boys had 39 erasers left, how many erasers did Henry have in the end?

	Henry	Ryan	Japheth	Total
Comparing Ryan and Japheth at first		4 u	5 u
Before	2 p	2x2 = 4 u	5 u	58
Change	- 1 p	-1x2 = - 2 u		- 19
After	1 p	1x2 = 2 u	5 u	39

Total number of erasers that Henry and Ryan gave away
= 58 - 39
= 19

The number of erasers that Ryan had at first is repeated.  Make the number of erasers that Ryan had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 58 - 39
1 p + 2 u = 19
1 p = 19 - 2 u --- (1)

1 p + 2 u + 5 u = 39
1 p + 7 u = 39
1 p = 39 - 7 u --- (2)

(1) = (2)
19 - 2 u = 39 - 7 u
7 u - 2 u = 39 - 19
7 u - 2 u = 20
5 u = 20

1 u = 20 ÷ 5 = 4

Substitute 1 u = 4 into (1).
1 p = 19 - 2 u
1 p = 19 - 2 x 4
1 p = 19 - 8

1 p = 11

Number of erasers that Henry had in the end
= 1 p
= 11

Answer(s): 11