Lucy had 25% more marbles than Anthony. Jack had 50% fewer marbles than Lucy. Lucy and Anthony gave Jack some marbles in the ratio of 3 : 4. As a result, Jack had 60% more marbles than before. Given that Anthony had 60 less marbles than Jack in the end, how many marbles did Anthony give to Jack?

Lucy	Anthony	Jack
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Lucy : Anthony = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Lucy : Jack = 2 : 1

The number of marbles that Lucy had at first is repeated. Make the number of marbles that Lucy had at first the same.  LCM of 5 and 2 is 10.

	Lucy	Anthony	Jack
Before	10x7 =  70 u	8x7 = 56 u	5x7 = 35 u
Change			+ 3x7 = + 21 u
Comparing the changes in the number of marbles	- 3x3 = - 9 u	- 4x3 = - 12 u	+ 7x3 = + 21 u
After	61 u	44 u	8x7 = 56 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of marbles that Lucy and Anthony gave to Jack is repeated.  Make the total number of marbles that Lucy and Anthony gave to Jack the same.  LCM of 7 and 3 is 21.

Number of marbles that Anthony had less than Jack 
= 56 u - 44 u
= 12 u

12 u = 60

1 u = 60 ÷ 12 = 5

Number of marbles that Anthony gave to Jack
= 12 u
= 12 x 5
= 60

Answer(s): 60