You are charged $419 for a new bicycle. Assume sales tax is 6.9%, what was the original price for the bicycle? (round your answer to the nearest cent)
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Understanding Sales Tax Calculation**
When you purchase an item with a sales tax, the amount you pay includes the original price of the item plus the sales tax. Given this, we can reverse the calculation to find the original price if we know the final price and the tax rate.
### Problem:
You are charged $419 for a new bicycle. Assume sales tax is 6.9%. What was the original price for the bicycle? (round your answer to the nearest cent)
### Method:
1. Denote the original price of the bicycle as \( P \).
2. The sales tax rate is 6.9%, which means the price with tax is \( P + 0.069P = 1.069P \).
3. We know the total price is $419, hence:
\[
1.069P = 419
\]
4. To find \( P \), divide both sides by 1.069:
\[
P = \frac{419}{1.069}
\]
### Calculation:
\[
P = \frac{419}{1.069} \approx 392.42
\]
### Solution:
The original price of the bicycle was approximately **$392.42**.
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