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

Yoko	Sarah	Julie
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Sarah	Julie	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 Sarah and Julie have
= 52 u + 40 u
= 92 u

After Sarah gives to Julie, both of them will have the same number of buttons. 

The total number of buttons that Sarah and Julie have remains unchanged.

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

Number of buttons that Sarah gives to Julie
= 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