Fanny has 30% as many buttons as Roshel. Roshel has 140% as many buttons as Nora. If Roshel gives 60 buttons to Nora, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Fanny	Roshel	Nora
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Roshel	Nora	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 Roshel and Nora have
= 70 u + 50 u
= 120 u

After Roshel gives to Nora, both of them will have the same number of buttons. 

The total number of buttons that Roshel and Nora have remains unchanged.

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

Number of buttons that Roshel gives to Nora
= 70 u - 60 u
= 10 u

10 u = 60

1 u = 60 ÷ 10 = 6

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 6
= 282

Answer(s): 282