Albert and Caden had 87 marbles in total. Caden had 45 marbles more than Albert at first. After Albert and Caden played a game with Kimberly, Albert had ¹₆ as many marbles as Caden. If Albert lost as many marbles as Caden to Kimberly, find the number of marbles that Albert lost to Kimberly.

	Albert	Caden	Difference
Before	1 u	1 u + 45	45
Change	- ?	- ?
After	1 p	6 p	5 p

Total number of marbles at first
= 1 u + 1 u + 45 
= 2 u + 45

2 u + 45 = 87
2 u = 87 - 45
2 u = 42

1 u = 42 ÷ 2 = 21

Since Albert lost the same number of marbles as Caden, the difference in the number of marbles between Albert and Caden at first and in the end remains the same.

Difference in the number of marbles in the end
= 6 p - 1 p
= 5 p

5 p = 45

1 p = 45 ÷ 5 = 9

Number of marbles that Albert lost to Kimberly
= 1 u - 1 p
= 21 - 1 x 9
= 21 - 9
= 12

Answer(s): 12