the price of a pen was reduced in two stages. in the first stage was reduced with ten dollars and in the second stage was reduced with ten percent. the final price of the pen is 27 dollars. find the initial price of the pen

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.

The price of a pen was reduced in two stages. In the first stage, it was reduced by ten dollars, and in the second stage, it was reduced by ten percent. The final price of the pen is 27 dollars. Find the initial price of the pen.

Learn how to calculate the initial price of a pen reduced in two stages: first by $10 and then by 10%. With the final price of $27, this problem involves algebra and percentage calculations, suitable for students in Grades 7-9.

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