Francis heard that a car stereo system was on sale for 30% off. If the sale price was $57.75, what was the original price of the stereo? (needs proportion, work and solution)
The correct answer and explanation is:
To solve this problem, we can use a proportion to find the original price of the stereo.
Let the original price of the stereo be represented by xx.
The stereo is on sale for 30% off, meaning the sale price is 70% of the original price, because 100% – 30% = 70%. Therefore, the relationship between the original price and the sale price can be written as: 70100=57.75x\frac{70}{100} = \frac{57.75}{x}
This proportion states that 70% of the original price equals the sale price of $57.75. To solve for xx, we can cross-multiply: 70×x=100×57.7570 \times x = 100 \times 57.75
Simplifying the right-hand side: 70x=577570x = 5775
Now, divide both sides of the equation by 70 to isolate xx: x=577570x = \frac{5775}{70} x=82.50x = 82.50
Thus, the original price of the stereo was $82.50.
Explanation:
The problem is based on applying a proportion to represent the relationship between the sale price and the original price. Since the stereo was on sale for 30% off, the sale price was 70% of the original price. Setting up a proportion allows us to solve for the original price algebraically. After cross-multiplying and simplifying, we find the original price to be $82.50. This approach of using proportions is a common way to solve percentage-based price discount problems.