Carl and Owen had 58 marbles in total. Owen had 10 marbles more than Carl at first. After Carl and Owen played a game with Rachel, Carl had ⁷₁₂ as many marbles as Owen. If Carl lost as many marbles as Owen to Rachel, find the number of marbles that Carl lost to Rachel.

	Carl	Owen	Difference
Before	1 u	1 u + 10	10
Change	- ?	- ?
After	7 p	12 p	5 p

Total number of marbles at first
= 1 u + 1 u + 10 
= 2 u + 10

2 u + 10 = 58
2 u = 58 - 10
2 u = 48

1 u = 48 ÷ 2 = 24

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

Difference in the number of marbles in the end
= 12 p - 7 p
= 5 p

5 p = 10

1 p = 10 ÷ 5 = 2

Number of marbles that Carl lost to Rachel
= 1 u - 7 p
= 24 - 7 x 2
= 24 - 14
= 10

Answer(s): 10