Caden, Albert and Luke had a total of 59 stickers. The ratio of Albert's stickers to Luke's stickers was 4 : 3 at first. Caden and Albert each gave away ¹₂ of their stickers. Given that the three boys had 37 stickers left, how many stickers did Caden have at first?

	Caden	Albert	Luke	Total
Comparing Albert and Luke at first		4 u	3 u
Before	2 p	2x2 = 4 u	3 u	59
Change	- 1 p	-1x2 = - 2 u		- 22
After	1 p	1x2 = 2 u	3 u	37

Total number of stickers that Caden and Albert gave away
= 59 - 37
= 22

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

1 p + 2 u = 59 - 37
1 p + 2 u = 22
1 p = 22 - 2 u --- (1)

1 p + 2 u + 3 u = 37
1 p + 5 u = 37
1 p = 37 - 5 u --- (2)

(1) = (2)
22 - 2 u = 37 - 5 u
5 u - 2 u = 37 - 22
5 u - 2 u = 15
3 u = 15

1 u = 15 ÷ 3 = 5

Substitute 1 u = 5 into (1).
1 p = 22 - 2 u
1 p = 22 - 2 x 5
1 p = 22 - 10

1 p = 12

Number of stickers that Caden had at first
= 2 p
= 2 x 12
= 24

Answer(s): 24