a price of a good is raised 9%, then later reduced 8%. Later the price was reduced 39% more. What was the original price of the good when the price now is 838,50? Give the answer with 2 decimals.

To find the original price of the good, we can reverse the percentage changes step by step. Here's the solution:

### Step 1: Consider the final reduction of 39%.
Let \( P_f \) be the price after the 8% reduction and before the 39% reduction. Since the price was reduced by 39%, the current price \( P_c = 838.50 \) is 61% of \( P_f \) (because \( 100\% - 39\% = 61\% \)).

So, \( P_f = \frac{838.50}{0.61} \).

### Step 2: Find the price before the 39% reduction.
\[
P_f = \frac{838.50}{0.61} \approx 1374.59
\]

### Step 3: Consider the previous 8% reduction.
The price \( P_r \) before this reduction was 100% of its value, but after the reduction, it became 92% of \( P_r \). So,
\[
P_r = \frac{1374.59}{0.92} \approx 1494.12
\]

### Step 4: Consider the initial 9% increase.
Before the initial 9% increase, the original price \( P_o \) was 100% of its value, and after the increase, it became 109% of \( P_o \). So,
\[
P_o = \frac{1494.12}{1.09} \approx 1371.12
\]

### Final Answer:
The original price of the good was **1371.12**.

Would you like any more details or have any questions about this calculation? Here are five related questions you might find interesting:

1. How would the original price change if the reductions were applied in a different order?
2. What would be the final price if the original price was 1371.12 but the price increases were 12% and 8% instead?
3. How does the order of percentage increases and decreases affect the final price?
4. How would you calculate the final price if there was an additional percentage increase after the final reduction?
5. What would be the new price if the last reduction was 45% instead of 39%?

**Tip:** When reversing percentage changes, always work backward step by step to avoid confusion.

Learn how to calculate the original price of a good after it was raised by 9% and then reduced by 8% and 39% more, resulting in the final price of 838.50. Follow a step-by-step solution involving percentage calculations and reverse percentage changes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation