If the total number of shares in 2004 is 1750 more than the average number of shares in 2003 and 2006, then find the average number of shares from 2001 to 2006 given the following data:

- Shares in 2001: 10000
- Shares in 2002: 12000
- Shares in 2003: 30000
- Shares in 2006: 25000 (with 90% of this value considered for calculation)

Calculate the average number of shares from 2001 to 2006.

Question

If the total number of shares in 2004 is 1750 more than the average number of shares in 2003 and 2006, then find the average number of shares from 2001 to 2006 given the following data:

- Shares in 2001: 10000
- Shares in 2002: 12000
- Shares in 2003: 30000
- Shares in 2006: 25000 (with 90% of this value considered for calculation)

Calculate the average number of shares from 2001 to 2006.

Accepted Answer

**Solution:**

1. Calculate total shares in 2006 considering 90% of 25000:
   $$ 25000 	imes \frac{90}{100} = 22500 $$

2. Average number of shares in 2003 and 2006:
   $$ \frac{30000 + 22500}{2} = \frac{52500}{2} = 26250 $$

3. Total shares in 2004 is 1750 more than this average:
   $$ 26250 + 1750 = 28000 $$

4. Given shares for other years:
   - 2001: 10000
   - 2002: 12000
   - 2003: 30000
   - 2004: 28000 (calculated)
   - 2005: 25000
   - 2006: 22500 (calculated)

5. Calculate the average number of shares from 2001 to 2006:
   $$ \frac{10000 + 12000 + 30000 + 28000 + 25000 + 22500}{6} = \frac{127500}{6} = 21250 $$

**Answer:** 21250

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