Jack had 25% more buttons than Anna. Robert had 50% fewer buttons than Jack. Jack and Anna gave Robert some buttons in the ratio of 3 : 5. As a result, Robert had 60% more buttons than before. Given that Robert had 120 more buttons than Anna in the end, how many buttons did Jack give to Robert?

Jack	Anna	Robert
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Jack : Anna = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Jack : Robert = 2 : 1

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

	Jack	Anna	Robert
Before	10x8 =  80 u	8x8 = 64 u	5x8 = 40 u
Change			+ 3x8 = + 24 u
Comparing the changes in the number of buttons	- 3x3 = - 9 u	- 5x3 = - 15 u	+ 8x3 = + 24 u
After	71 u	49 u	8x8 = 64 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of buttons that Jack and Anna gave to Robert is repeated.  Make the total number of buttons that Jack and Anna gave to Robert the same.  LCM of 8 and 3 is 24.

Number of buttons that Robert had more than Anna 
= 64 u - 49 u
= 15 u

15 u = 120

1 u = 120 ÷ 15 = 8

Number of buttons that Jack gave to Robert
= 9 u
= 9 x 8
= 72

Answer(s): 72