Anna has 30% as many buttons as Rachel. Rachel has 140% as many buttons as Elyse. If Rachel gives 20 buttons to Elyse, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Anna	Rachel	Elyse
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Rachel	Elyse	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 Rachel and Elyse have
= 70 u + 50 u
= 120 u

After Rachel gives to Elyse, both of them will have the same number of buttons. 

The total number of buttons that Rachel and Elyse have remains unchanged.

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

Number of buttons that Rachel gives to Elyse
= 70 u - 60 u
= 10 u

10 u = 20

1 u = 20 ÷ 10 = 2

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 2
= 94

Answer(s): 94