Xylia has 30% as many buttons as Elyse. Elyse has 110% as many buttons as Risa. If Elyse gives 20 buttons to Risa, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Xylia	Elyse	Risa
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

The number of buttons that Xylia has is repeated.  Make the number of buttons that Xylia has the same. LCM of 10 and 11 is 110.

	Elyse	Risa	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of buttons that Elyse and Risa have
= 110 u + 100 u
= 210 u

After Elyse gives to Risa, both of them will have the same number of buttons. 

The total number of buttons that Elyse and Risa have remains unchanged.

Number of buttons that each of them will have
= 210 u ÷ 2
= 105 u

Number of buttons that Elyse gives to Risa
= 110 u - 105 u
= 5 u

5 u = 20

1 u = 20 ÷ 5 = 4

Total number of buttons that three of them have
= 210 u + 33 u
= 243 u

Average number of buttons that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 4
= 324

Answer(s): 324