Albert, Owen and Henry had a total of 137 pencils. The ratio of Owen's pencils to Henry's pencils was 8 : 5 at first. Albert and Owen each gave away ¹₂ of their pencils. Given that the three boys had 91 pencils left, how many pencils did Albert have in the end?

	Albert	Owen	Henry	Total
Comparing Owen and Henry at first		8 u	5 u
Before	2 p	2x4 = 8 u	5 u	137
Change	- 1 p	-1x4 = - 4 u		- 46
After	1 p	1x4 = 4 u	5 u	91

Total number of pencils that Albert and Owen gave away
= 137 - 91
= 46

The number of pencils that Owen had at first is repeated.  Make the number of pencils that Owen had at first the same.  LCM of 8 and 2 is 8.

1 p + 4 u = 137 - 91
1 p + 4 u = 46
1 p = 46 - 4 u --- (1)

1 p + 4 u + 5 u = 91
1 p + 9 u = 91
1 p = 91 - 9 u --- (2)

(1) = (2)
46 - 4 u = 91 - 9 u
9 u - 4 u = 91 - 46
9 u - 4 u = 45
5 u = 45

1 u = 45 ÷ 5 = 9

Substitute 1 u = 9 into (1).
1 p = 46 - 4 u
1 p = 46 - 4 x 9
1 p = 46 - 36

1 p = 10

Number of pencils that Albert had in the end
= 1 p
= 10

Answer(s): 10