Wendy has 30% as many buttons as Zara. Zara has 110% as many buttons as Gem. If Zara gives 15 buttons to Gem, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Wendy	Zara	Gem
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Zara	Gem	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 Zara and Gem have
= 110 u + 100 u
= 210 u

After Zara gives to Gem, both of them will have the same number of buttons. 

The total number of buttons that Zara and Gem have remains unchanged.

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

Number of buttons that Zara gives to Gem
= 110 u - 105 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

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 3
= 243

Answer(s): 243