To find the original price of a CD that is currently being sold with a 15% discount at a sale price of [tex]$34.85, follow these steps:
1. Understand the Problem:
- The sale price is given as $[/tex]34.85.
- The discount rate applied is 15%.
2. Express the Sale Price in Terms of the Original Price:
- The sale price is a result of the original price reduced by 15%. Mathematically, the sale price can be expressed as:
[tex]\[
\text{Sale Price} = \text{Original Price} \times (1 - \text{Discount Rate})
\][/tex]
3. Substitute the Known Values:
- Let the original price be denoted as [tex]\( P \)[/tex].
- The discount rate is 15%, which is equivalent to 0.15 in decimal form.
- Plugging the given values into the equation:
[tex]\[
34.85 = P \times (1 - 0.15)
\][/tex]
4. Simplify the Expression:
[tex]\[
34.85 = P \times 0.85
\][/tex]
5. Solve for the Original Price [tex]\( P \)[/tex]:
- Isolate [tex]\( P \)[/tex] by dividing both sides of the equation by 0.85:
[tex]\[
P = \frac{34.85}{0.85}
\][/tex]
6. Calculate the Original Price:
[tex]\[
P = 41.0
\][/tex]
7. Round to the Nearest Cent:
- In this case, the calculation results in the original price being exactly [tex]$41.00, so no further rounding is necessary.
So, the original price of the CD was $[/tex]41.00.
