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

Winnie	Opal	Elyse
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Opal	Elyse	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 Opal and Elyse have
= 110 u + 100 u
= 210 u

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

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

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

Number of buttons that Opal gives to Elyse
= 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