Kathy has 25% as many coins as Shiyun. Shiyun has 130% as many coins as Penelope. If Shiyun gives 54 coins to Penelope, both will then have an equal number of coins. Find the average number of coins the three of them have.

Kathy	Shiyun	Penelope
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

The number of coins that Kathy has is repeated.  Make the number of coins that Kathy has the same. LCM of 4 and 13 is 52.

	Shiyun	Penelope	Total
Before	52 u	40 u	92 u
Change	- 6 u	+ 6 u
After	46 u	46 u	92 u

Total number of coins that Shiyun and Penelope have
= 52 u + 40 u
= 92 u

After Shiyun gives to Penelope, both of them will have the same number of coins. 

The total number of coins that Shiyun and Penelope have remains unchanged.

Number of coins that each of them will have
= 92 u ÷ 2
= 46 u

Number of coins that Shiyun gives to Penelope
= 52 u - 46 u
= 6 u

6 u = 54

1 u = 54 ÷ 6 = 9

Total number of coins that three of them have
= 92 u + 13 u
= 105 u

Average number of coins that each of them have
= 105 u ÷ 3
= 35 u
= 35 x 9
= 315

Answer(s): 315