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

Emily	Anna	Tammy
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Anna	Tammy	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 Anna and Tammy have
= 110 u + 100 u
= 210 u

After Anna gives to Tammy, both of them will have the same number of buttons. 

The total number of buttons that Anna and Tammy have remains unchanged.

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

Number of buttons that Anna gives to Tammy
= 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