Ben, Billy and Tommy had some marbles. Billy had 40% more marbles than Ben. Billy had ³₅ of Tommy's. After Ben gave 30 marbles to Billy, he had ¹₃ of what Billy had. How many more marbles did Tommy have than Billy in the end?

Ben	Billy	Tommy
5x3	7x3
	3x7	5x7
15	21	35

	Tommy	Ben	Billy	Total marbles of  Ben and Billy
Before	35x1 = 35 u	15x1 = 15 u	21x1 = 21 u	36x1 = 36 u
Change		- 30	+ 30
After	35 u	1x9 = 9 u	3x9 = 27 u	4x9 = 36 u

Number of marbles that Billy had more than Ben at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Ben : Billy = 5 : 7

The number of marbles that Billy had at first is repeated.  Make the number of marbles that Billy had at first the same.  LCM of 7 and 3 is 21.

When Ben gave 30 marbles to Billy, the total number of marbles that Billy and Ben had at first and in the end remains the same.  Make the total number of marbles that Billy and Ben had the same.  LCM of 36 and 4 is 36.

Number of marbles that Ben gave to Billy
= 15 u - 9 u
= 6 u

6 u = 30

1 u = 30 ÷ 6 = 5

Number of marbles that Tommy had more than Billy in the end
= 35 u - 27 u
= 8 u
= 8 x 5
= 40

Answer(s): 40