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

Winnie	Nora	Kylie
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.

	Nora	Kylie	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 Nora and Kylie have
= 110 u + 100 u
= 210 u

After Nora gives to Kylie, both of them will have the same number of buttons. 

The total number of buttons that Nora and Kylie have remains unchanged.

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

Number of buttons that Nora gives to Kylie
= 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