Japheth, Brandon and Bobby had a total of 176 pens. The ratio of Brandon's pens to Bobby's pens was 8 : 5 at first. Japheth and Brandon each gave away ¹₂ of their pens. Given that the three boys had 118 pens left, how many pens did Japheth have at first?

	Japheth	Brandon	Bobby	Total
Comparing Brandon and Bobby at first		8 u	5 u
Before	2 p	2x4 = 8 u	5 u	176
Change	- 1 p	-1x4 = - 4 u		- 58
After	1 p	1x4 = 4 u	5 u	118

Total number of pens that Japheth and Brandon gave away
= 176 - 118
= 58

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

1 p + 4 u = 176 - 118
1 p + 4 u = 58
1 p = 58 - 4 u --- (1)

1 p + 4 u + 5 u = 118
1 p + 9 u = 118
1 p = 118 - 9 u --- (2)

(1) = (2)
58 - 4 u = 118 - 9 u
9 u - 4 u = 118 - 58
9 u - 4 u = 60
5 u = 60

1 u = 60 ÷ 5 = 12

Substitute 1 u = 12 into (1).
1 p = 58 - 4 u
1 p = 58 - 4 x 12
1 p = 58 - 48

1 p = 10

Number of pens that Japheth had at first
= 2 p
= 2 x 10
= 20

Answer(s): 20