Problem 70 - Introductory Algebra for College Students

Question

A fax machine regularly sells for \(\$ 380 .\) The sale price is \(\$ 266\). Find the percent decrease in the machine's price.

Step-by-Step Solution

Answer

The percent decrease in the machine's price is 30%.

Step 1: Calculate the Difference in Price

Subtract the sale price (\$266) from the regular price (\$380). This gives the amount by which the price has decreased: \$380 - \$266 = \$114.

Step 2: Calculate the Ratio of Decrease to Original Price

Divide the price decrease (\$114) by the original price (\$380). This gives the ratio of the price decrease to the original price: \$114 / \$380 = 0.3.

Step 3: Convert the Ratio to a Percentage

Multiply the ratio (0.3) by 100 to convert it to a percentage:. 0.3 * 100 = 30. The percent decrease in the machine's price is 30%.

Key Concepts

Ratio Calculation

To understand how to find a ratio, let's first look at the components involved. When determining the percent decrease in price, the ratio is the relationship between the price decrease and the original price.
To calculate this, you subtract the new sale price from the original price to find the amount the price has decreased. Then, you divide this number by the original price.
In mathematical terms, the formula looks like this:

• Ratio of decrease = \( \frac{\text{Price Decrease}}{\text{Original Price}} \)

In the given problem, we calculated the price decrease as \( \\(380 - \\)266 = \\(114 \) and the ratio as \( \frac{\\)114}{\$380} = 0.3 \).
This number tells us how the decrease compares to the original price, which is pivotal in understanding percentage conversion.

Price Decrease

The concept of a price decrease is quite straightforward. It represents how much less something costs now compared to its original price. This is an essential calculation in understanding sales and discounts.
To calculate price decrease, you simply subtract the reduced price (or sale price) from the original price. This provides you with the exact amount by which the price has lowered.

• Price Decrease = Original Price - Sale Price

For the fax machine, the price decrease was calculated as \( \\(380 - \\)266 = \$114 \).
Recognizing and calculating price decrease is crucial, especially when comparing the savings from different sales or discounts.

Percentage Conversion

Converting a ratio into a percentage is a common mathematical task which clarifies how one quantity compares to another. A percentage expresses how a number relates to 100, making it easy to understand at a glance.
To convert a ratio to a percentage, you multiply the ratio by 100. This transformation gives a more tangible comprehension of data since percentages are a familiar way to represent proportions.
Use the formula below:

• Percentage = Ratio \( \times 100 \)

For our example, the ratio of the price decrease to the original price was 0.3. When you multiply this by 100, the result is 30%.This indicates the price has decreased by 30% from the original, making the sale price much more appealing. Understanding percentage conversions can significantly aid in interpreting data and making informed decisions regarding purchases.