Winnie has 30% as many buttons as Lynn. Lynn has 140% as many buttons as Raeann. If Lynn gives 110 buttons to Raeann, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Winnie	Lynn	Raeann
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

The number of buttons that Winnie has is repeated.  Make the number of buttons that Winnie has the same. LCM of 10 and 7 is 70.

	Lynn	Raeann	Total
Before	70 u	50 u	120 u
Change	- 10 u	+ 10 u
After	60 u	60 u	120 u

Total number of buttons that Lynn and Raeann have
= 70 u + 50 u
= 120 u

After Lynn gives to Raeann, both of them will have the same number of buttons. 

The total number of buttons that Lynn and Raeann have remains unchanged.

Number of buttons that each of them will have
= 120 u ÷ 2
= 60 u

Number of buttons that Lynn gives to Raeann
= 70 u - 60 u
= 10 u

10 u = 110

1 u = 110 ÷ 10 = 11

Total number of buttons that three of them have
= 120 u + 21 u
= 141 u

Average number of buttons that each of them have
= 141 u ÷ 3
= 47 u
= 47 x 11
= 517

Answer(s): 517