Mary has 25% as many buttons as Wendy. Wendy has 130% as many buttons as Yen. If Wendy gives 30 buttons to Yen, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Mary	Wendy	Yen
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Wendy	Yen	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 Wendy and Yen have
= 52 u + 40 u
= 92 u

After Wendy gives to Yen, both of them will have the same number of buttons. 

The total number of buttons that Wendy and Yen have remains unchanged.

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

Number of buttons that Wendy gives to Yen
= 52 u - 46 u
= 6 u

6 u = 30

1 u = 30 ÷ 6 = 5

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 5
= 175

Answer(s): 175