Archie and Oliver had 66 marbles in total. Archie had 30 marbles less than Oliver at first. After Archie and Oliver played a game with Kylie, Archie had ¹₁₁ as many marbles as Oliver. If Archie lost as many marbles as Oliver to Kylie, find the number of marbles that Oliver lost to Kylie.

	Archie	Oliver	Difference
Before	1 u	1 u + 30	30
Change	- ?	- ?
After	1 p	11 p	10 p

Total number of marbles at first
= 1 u + 1 u + 30 
= 2 u + 30

2 u + 30 = 66
2 u = 66 - 30
2 u = 36

1 u = 36 ÷ 2 = 18

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

Difference in the number of marbles in the end
= 11 p - 1 p
= 10 p

10 p = 30

1 p = 30 ÷ 10 = 3

Number of marbles that Archie lost to Kylie
= 1 u - 1 p
= 18 - 1 x 3
= 18 - 3
= 15

Since Oliver lost the same number of marbles as Archie, the number of marbles that each lost to Kylie is the same.

Number of marbles that Oliver lost = 15

Answer(s): 15