Robert had 25% more cards than Levi. Tommy had 50% fewer cards than Robert. Robert and Levi gave Tommy some cards in the ratio of 4 : 5. As a result, Tommy had 60% more cards than before. Given that Levi had 45 less cards than Tommy in the end, how many cards did Levi give to Tommy?

Robert	Levi	Tommy
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Robert : Levi = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Robert : Tommy = 2 : 1

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

	Robert	Levi	Tommy
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of cards	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of cards that Robert and Levi gave to Tommy is repeated.  Make the total number of cards that Robert and Levi gave to Tommy the same.  LCM of 9 and 3 is 9.

Number of cards that Levi had less than Tommy 
= 24 u - 19 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of cards that Levi gave to Tommy
= 5 u
= 5 x 9
= 45

Answer(s): 45