To determine the original price of the stove before the increase, follow these steps:
1. Understand the Problem:
- The final price after the increase is [tex]\( R3,499.95 \)[/tex].
- The price has been increased by [tex]\( 12.9\% \)[/tex].
- We need to find the original price before this increase and then round it to the nearest R100.
2. Define the Relationships:
- Let the original price be [tex]\( P \)[/tex].
- The final price is after a [tex]\( 12.9\% \)[/tex] increase on the original price.
- The final price can be expressed as:
[tex]\[
\text{Final Price} = \text{Original Price} + \text{Increase}
\][/tex]
- The increase itself is [tex]\( 12.9\% \)[/tex] of the original price:
[tex]\[
\text{Increase} = 0.129 \times P
\][/tex]
- Therefore, the final price formula becomes:
[tex]\[
3499.95 = P + 0.129 \times P
\][/tex]
3. Create an Equation:
- Combine the terms involving [tex]\( P \)[/tex]:
[tex]\[
3499.95 = P (1 + 0.129)
\][/tex]
- Simplify the equation:
[tex]\[
3499.95 = P (1.129)
\][/tex]
4. Solve for [tex]\( P \)[/tex]:
- Isolate [tex]\( P \)[/tex] by dividing both sides by [tex]\( 1.129 \)[/tex]:
[tex]\[
P = \frac{3499.95}{1.129}
\][/tex]
5. Calculate the Original Price:
- Perform the division:
[tex]\[
P \approx 3099.95
\][/tex]
6. Round to the Nearest R100:
- The nearest R100 to 3099.95 is [tex]\( R3,100 \)[/tex].
Therefore, the original price of the stove, rounded to the nearest R100, was [tex]\( R3,100 \)[/tex].
