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

Natalie	Wendy	Hilda
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Wendy	Hilda	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 Wendy and Hilda have
= 70 u + 50 u
= 120 u

After Wendy gives to Hilda, both of them will have the same number of buttons. 

The total number of buttons that Wendy and Hilda have remains unchanged.

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

Number of buttons that Wendy gives to Hilda
= 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