Kimberly has 30% as many buttons as Joelle. Joelle has 140% as many buttons as Vanessa. If Joelle gives 90 buttons to Vanessa, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Kimberly	Joelle	Vanessa
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Joelle	Vanessa	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 Joelle and Vanessa have
= 70 u + 50 u
= 120 u

After Joelle gives to Vanessa, both of them will have the same number of buttons. 

The total number of buttons that Joelle and Vanessa have remains unchanged.

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

Number of buttons that Joelle gives to Vanessa
= 70 u - 60 u
= 10 u

10 u = 90

1 u = 90 ÷ 10 = 9

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 9
= 423

Answer(s): 423