Nora has 25% as many buttons as Shiyun. Shiyun has 130% as many buttons as Xandra. If Shiyun gives 12 buttons to Xandra, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Nora	Shiyun	Xandra
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Shiyun	Xandra	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 Shiyun and Xandra have
= 52 u + 40 u
= 92 u

After Shiyun gives to Xandra, both of them will have the same number of buttons. 

The total number of buttons that Shiyun and Xandra have remains unchanged.

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

Number of buttons that Shiyun gives to Xandra
= 52 u - 46 u
= 6 u

6 u = 12

1 u = 12 ÷ 6 = 2

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 2
= 70

Answer(s): 70