Sarah has 30% as many buttons as Cindy. Cindy has 110% as many buttons as Irene. If Cindy gives 45 buttons to Irene, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Sarah	Cindy	Irene
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Cindy	Irene	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 Cindy and Irene have
= 110 u + 100 u
= 210 u

After Cindy gives to Irene, both of them will have the same number of buttons. 

The total number of buttons that Cindy and Irene have remains unchanged.

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

Number of buttons that Cindy gives to Irene
= 110 u - 105 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

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 9
= 729

Answer(s): 729