Elyse has 30% as many buttons as Nora. Nora has 110% as many buttons as Jade. If Nora gives 40 buttons to Jade, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Elyse	Nora	Jade
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

The number of buttons that Elyse has is repeated.  Make the number of buttons that Elyse has the same. LCM of 10 and 11 is 110.

	Nora	Jade	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of buttons that Nora and Jade have
= 110 u + 100 u
= 210 u

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

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

Number of buttons that each of them will have
= 210 u ÷ 2
= 105 u

Number of buttons that Nora gives to Jade
= 110 u - 105 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Total number of buttons that three of them have
= 210 u + 33 u
= 243 u

Average number of buttons that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 8
= 648

Answer(s): 648