Mary has 30% as many pens as Nicole. Nicole has 110% as many pens as Dana. If Nicole gives 45 pens to Dana, both will then have an equal number of pens. Find the average number of pens the three of them have.

Mary	Nicole	Dana
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Nicole	Dana	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of pens that Nicole and Dana have
= 110 u + 100 u
= 210 u

After Nicole gives to Dana, both of them will have the same number of pens. 

The total number of pens that Nicole and Dana have remains unchanged.

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

Number of pens that Nicole gives to Dana
= 110 u - 105 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

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

Average number of pens that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 9
= 729

Answer(s): 729