Linda has 30% as many buttons as Pamela. Pamela has 110% as many buttons as Natalie. If Pamela gives 30 buttons to Natalie, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Linda	Pamela	Natalie
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Pamela	Natalie	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 Pamela and Natalie have
= 110 u + 100 u
= 210 u

After Pamela gives to Natalie, both of them will have the same number of buttons. 

The total number of buttons that Pamela and Natalie have remains unchanged.

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

Number of buttons that Pamela gives to Natalie
= 110 u - 105 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

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 6
= 486

Answer(s): 486