Eva has 25% as many buttons as Natalie. Natalie has 130% as many buttons as Raeann. If Natalie gives 36 buttons to Raeann, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Eva	Natalie	Raeann
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Natalie	Raeann	Total
Before	52 u	40 u	92 u
Change	- 6 u	+ 6 u
After	46 u	46 u	92 u

Total number of buttons that Natalie and Raeann have
= 52 u + 40 u
= 92 u

After Natalie gives to Raeann, both of them will have the same number of buttons. 

The total number of buttons that Natalie and Raeann have remains unchanged.

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

Number of buttons that Natalie gives to Raeann
= 52 u - 46 u
= 6 u

6 u = 36

1 u = 36 ÷ 6 = 6

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

Average number of buttons that each of them have
= 105 u ÷ 3
= 35 u
= 35 x 6
= 210

Answer(s): 210