Ivory has 30% as many buttons as Jane. Jane has 110% as many buttons as Eva. If Jane gives 55 buttons to Eva, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Ivory	Jane	Eva
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Jane	Eva	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 Jane and Eva have
= 110 u + 100 u
= 210 u

After Jane gives to Eva, both of them will have the same number of buttons. 

The total number of buttons that Jane and Eva have remains unchanged.

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

Number of buttons that Jane gives to Eva
= 110 u - 105 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

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 11
= 891

Answer(s): 891