Caden, Peter and Cole had some marbles. Peter had 60% more marbles than Caden. Peter had ⁴₇ of Cole's. After Caden gave 14 marbles to Peter, he had ¹₂ of what Peter had. How many more marbles did Cole have than Peter in the end?

Caden	Peter	Cole
5x1	8x1
	4x2	7x2
5	8	14

	Cole	Caden	Peter	Total marbles of  Caden and Peter
Before	14x3 = 42 u	5x3 = 15 u	8x3 = 24 u	13x3 = 39 u
Change		- 14	+ 14
After	42 u	1x13 = 13 u	2x13 = 26 u	3x13 = 39 u

Number of marbles that Peter had more than Caden at first in percent
= 100%+ 60%
= 160%

160% = ¹⁶⁰₁₀₀ = ⁸₅

Caden : Peter = 5 : 8

The number of marbles that Peter had at first is repeated.  Make the number of marbles that Peter had at first the same.  LCM of 8 and 4 is 8.

When Caden gave 14 marbles to Peter, the total number of marbles that Peter and Caden had at first and in the end remains the same.  Make the total number of marbles that Peter and Caden had the same.  LCM of 13 and 3 is 39.

Number of marbles that Caden gave to Peter
= 15 u - 13 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of marbles that Cole had more than Peter in the end
= 42 u - 26 u
= 16 u
= 16 x 7
= 112

Answer(s): 112