In December, the price of a television in a shop was £P.
At the start of January, the price was reduced by £350.
At the start of February, the price was further reduced by 30% of the January price.
After the two reductions, the overall decrease in the price of the television was 44%.
What was P?
a) 625
b) 750
c) 1540
d) 1750
e) 2100

Let's solve the problem step by step.

1. **Initial Setup**:
   - The original price of the television in December was £P.

2. **First Reduction**:
   - In January, the price was reduced by £350. 
   - So, the price after the first reduction was \( P - 350 \).

3. **Second Reduction**:
   - In February, the price was reduced by 30% of the January price.
   - Therefore, the new price after the second reduction was:
     \[
     (P - 350) - 0.30 \times (P - 350)
     \]
   - Simplifying this:
     \[
     (P - 350)(1 - 0.30) = (P - 350) \times 0.70 = 0.7(P - 350)
     \]

4. **Overall Decrease**:
   - After the two reductions, the overall decrease in price was 44% of the original price.
   - So, the price after both reductions is:
     \[
     P - 0.44P = 0.56P
     \]
   - Setting the equation for the final price after two reductions:
     \[
     0.7(P - 350) = 0.56P
     \]

5. **Solve for P**:
   - Expanding the equation:
     \[
     0.7P - 245 = 0.56P
     \]
   - Subtract \( 0.56P \) from both sides:
     \[
     0.7P - 0.56P = 245
     \]
   - Simplify:
     \[
     0.14P = 245
     \]
   - Divide by 0.14:
     \[
     P = \frac{245}{0.14} = 1750
     \]

The value of \( P \) is **1750**, so the correct answer is **(d) 1750**.

Would you like more details or have any questions? Here are five related questions to expand on this concept:

1. How would the problem change if the overall reduction was 50% instead of 44%?
2. What would be the final price of the television after both reductions?
3. How can you determine the original price if only the final price and percentage reductions are given?
4. If the initial price reduction was a percentage instead of a fixed amount, how would the solution change?
5. What happens to the overall percentage decrease if the reductions are applied in a different order?

**Tip:** When solving percentage decrease problems, break down the problem into smaller steps and apply reductions sequentially.

Learn how to solve a problem involving the decrease in the price of a television over two stages of reduction, including fixed and percentage reductions. Understand the application of percentage decrease formulas and solve for the original price using algebraic equations. Suitable for advanced high school students (Grades 10-12).

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