Let the initial price of the pen be denoted by $P$.

Step 1: First reduction

The pen's price is reduced by $10, so the price after the first reduction becomes: $P - 10$

Step 2: Second reduction

After the first reduction, the price is further reduced by 10%. This means the new price becomes 90% of the price after the first reduction: $0.9 \times (P - 10)$

Step 3: Final price

We are given that the final price is $27, so: $0.9 \times (P - 10) = 27$

Step 4: Solve for $P$

1. Divide both sides of the equation by 0.9: $P - 10 = \frac{27}{0.9} = 30$
2. Add 10 to both sides: $P = 30 + 10 = 40$

Thus, the initial price of the pen is $40.

Would you like any further details or clarifications?

Here are 5 related questions to explore:

1. What if the percentage reduction in the second stage was 15% instead of 10%?
2. How would the problem change if the first reduction was a percentage instead of a fixed amount?
3. Can you solve the problem if the final price and both reductions were given as percentages?
4. How do you calculate the price if a percentage increase is followed by a percentage decrease?
5. How can you find the original price if only the final price and overall percentage reduction are known?

Tip: When solving price reduction problems, always apply the fixed amount reduction first, then the percentage reduction to the new amount.