A store reduces the price of a CD player by 20% and then reduces that price by 15%. If the final price of the CD player is $170, what was its original price?

Options

A. 140
B. 185
C. 200
D. 250

Answer

To find the original price of the CD player before the reductions, we can follow these steps:

### Step 1: Define the original price
Let the original price of the CD player be \( x \).

### Step 2: Calculate the price after the first reduction
The store reduces the price by 20%. Therefore, the remaining price after the first reduction is:
\[ \text{Price after first reduction} = x - 0.20x = 0.80x \]

### Step 3: Calculate the price after the second reduction
Next, the store reduces the new price by 15%. The remaining price after this second reduction is:
\[ \text{Price after second reduction} = 0.80x - 0.15(0.80x) = 0.80x \times 0.85 = 0.68x \]

### Step 4: Set up the equation with the final price
According to the problem, the final price after both reductions is $170. Therefore, we can set up the equation:
\[ 0.68x = 170 \]

### Step 5: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{170}{0.68} \]
Calculating this gives:
\[ x = 250 \]

### Conclusion
The original price of the CD player was **$250**.

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