Xylia has 30% as many buttons as Mary. Mary has 110% as many buttons as Emma. If Mary gives 40 buttons to Emma, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Xylia	Mary	Emma
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.

	Mary	Emma	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 Mary and Emma have
= 110 u + 100 u
= 210 u

After Mary gives to Emma, both of them will have the same number of buttons. 

The total number of buttons that Mary and Emma have remains unchanged.

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

Number of buttons that Mary gives to Emma
= 110 u - 105 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

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 8
= 648

Answer(s): 648