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

Rachel	Pamela	Shannon
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Pamela	Shannon	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 Shannon have
= 110 u + 100 u
= 210 u

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

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

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

Number of buttons that Pamela gives to Shannon
= 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