Diana has 30% as many stamps as Kathy. Kathy has 110% as many stamps as Zara. If Kathy gives 35 stamps to Zara, both will then have an equal number of stamps. Find the average number of stamps the three of them have.

Diana	Kathy	Zara
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Kathy	Zara	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of stamps that Kathy and Zara have
= 110 u + 100 u
= 210 u

After Kathy gives to Zara, both of them will have the same number of stamps. 

The total number of stamps that Kathy and Zara have remains unchanged.

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

Number of stamps that Kathy gives to Zara
= 110 u - 105 u
= 5 u

5 u = 35

1 u = 35 ÷ 5 = 7

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

Average number of stamps that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 7
= 567

Answer(s): 567