Gillian has 30% as many buttons as Xylia. Xylia has 110% as many buttons as Sabrina. If Xylia gives 10 buttons to Sabrina, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Gillian	Xylia	Sabrina
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Xylia	Sabrina	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 Xylia and Sabrina have
= 110 u + 100 u
= 210 u

After Xylia gives to Sabrina, both of them will have the same number of buttons. 

The total number of buttons that Xylia and Sabrina have remains unchanged.

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

Number of buttons that Xylia gives to Sabrina
= 110 u - 105 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

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 2
= 162

Answer(s): 162