Question

Business: Discount Pricing A store sells refurbished iPhones that cost \(12 \%\) less than the original price. If the new price of a refurbished iPhone is 572 dollar, what was the original price? How much is saved by purchasing the refurbished phone?

Short answer

The original price was 650 dollars. The savings amount to 78 dollars.

Step-by-step solution

- Set up the equation

Let the original price of the iPhone be denoted as \( x \). Since a refurbished iPhone costs \(12\%\) less than the original price, we can write the equation as \[ \text{New Price} = \text{Original Price} - (12\text{\% of Original Price}) \] or \[ 572 = x - 0.12x \]

- Simplify the equation

Combine the terms involving \( x \): \[ 572 = 0.88x \]

- Solve for the original price

Divide both sides of the equation by \( 0.88 \): \[ x = \frac{572}{0.88} \] Calculate the value of \( x \): \[ x = 650 \text{ dollars} \]

- Calculate the savings

Subtract the new price from the original price: \[ \text{Savings} = 650 - 572 = 78 \text{ dollars} \]

Key concepts

refurbished iPhones

Refurbished iPhones are pre-owned devices that have been returned, inspected, and restored to function like new. They often come with a warranty, making them a more reliable option compared to used phones bought from individual sellers. Purchasing refurbished iPhones often means significant cost savings, as these devices are sold at a discount compared to brand-new models.
Refurbished devices undergo rigorous testing and repair processes, ensuring they meet quality standards. This makes them an excellent choice for those seeking affordability without compromising on quality.

original price calculation

Calculating the original price of an item when given a discounted price involves understanding the relationship between the discount and the original price. In the problem, the refurbished iPhone is priced at 572 dollars, which is 12% less than its original price.
We set up the equation to represent this relationship:

• Let the original price be denoted by x.
• The new price is then given by: Original Price - (12% of Original Price)

So, the equation becomes:

• 572 = x - 0.12x
• 572 = 0.88x

Solving for x involves dividing 572 by 0.88 to find the original price. This calculation is fundamental for understanding how discounts affect pricing.

percentage discount

Understanding percentage discounts is crucial in many retail scenarios. A percentage discount represents a reduction in price by a certain percent.
For instance, a 12% discount on the original price means reducing the price by 12% of the original price.
Mathematically, this can be expressed as:

• Discount Amount = Original Price * (Discount Percentage)
• New Price = Original Price - Discount Amount

In our problem, the formula is expressed as:

• 572 = Original Price - 0.12 * Original Price

Knowing how to work with percentage discounts helps shoppers make informed decisions and understand their savings better.

savings calculation

Calculating savings from a discount involves determining the difference between the original price and the discounted price. This gives a clear idea of how much money was saved through the discount.
In our exercise, once we find the original price, which is 650 dollars, we can compute the savings by subtracting the new price from it:

• Savings = Original Price - Discounted Price

Substituting the values, we get:

• Savings = 650 - 572

This results in a savings of 78 dollars. Understanding this calculation is important for consumers to appreciate the benefits of discounts and better manage their spending.