Evan had 50% more cards than Emma. Harper had 20% fewer cards than Evan. Evan and Emma gave Harper some cards in the ratio of 1 : 3. As a result, Harper had 25% more cards than before. Given that Harper had 145 more cards than Emma in the end, how many cards did Evan give to Harper?

Evan	Emma	Harper
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Evan : Emma = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Evan : Harper = 5 : 4

The number of cards that Evan had at first is repeated. Make the number of cards that Evan had at first the same.  LCM of 3 and 5 is 15.

	Evan	Emma	Harper
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of cards	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	57 u	31 u	15x4 = 60 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of cards that Evan and Emma gave to Harper is repeated.  Make the total number of cards that Evan and Emma gave to Harper the same.  LCM of 4 and 3 is 12.

Number of cards that Harper had more than Emma 
= 60 u - 31 u
= 29 u

29 u = 145

1 u = 145 ÷ 29 = 5

Number of cards that Evan gave to Harper
= 3 u
= 3 x 5
= 15

Answer(s): 15