Problem 77 - Elementary Algebra

Question

The regular price of a portable GPS vehicle navigator is \(\$ 499.99\). The sale price is \(\$ 389.99\). Find the percent discount. Round to the nearest percent.

Step-by-Step Solution

Answer

The percent discount is 22%.

Step 1 - Determine the discount amount

Find the difference between the regular price and the sale price. This is done by subtracting the sale price from the regular price.Discount Amount = Regular Price - Sale Price = 499.99 - 389.99 = 110

Step 2 - Calculate the discount rate

To find the discount rate, divide the discount amount by the regular price and multiply by 100 to convert it to a percentage.Discount Rate = \(\frac{Discount Amount}{Regular Price} \times 100\)Substitute the values to get:Discount Rate = \(\frac{110}{499.99} \times 100\)

Step 3 - Perform the division and multiplication

First, divide 110 by 499.99:\(\frac{110}{499.99} \approx 0.220004\)Next, multiply by 100:\(0.220004 \times 100 \approx 22.00\)

Step 4 - Round to the nearest percent

Round the calculated percentage to the nearest whole number.22.00 rounds to 22%

Key Concepts

Understanding Algebraic Subtraction

In algebraic subtraction, we are simply taking one value and subtracting another from it. It helps us find the difference between two numbers.
Here's how you can do it:

• Write down the larger number first (in this case, the regular price of the GPS).
• Then, subtract the smaller number from it (the sale price).

In our exercise, the regular price is \$499.99\ and the sale price is \$389.99\. We subtract these:
\[ \text{Discount Amount} = 499.99 - 389.99 = 110 \] This difference, which is \$110\, is the amount saved during the discount.

Percentage Calculation

Calculating a percentage helps us understand what fraction or portion one number is of another. In our case, we want to know what percentage the discount amount is of the regular price.
We use the formula:
\[\text{Discount Rate} = \frac{\text{Discount Amount}}{\text{Regular Price}} \times 100\] Substituting the values from our problem, we get:

• Discount Amount = \$110
• Regular Price = \$499.99

So:
\[ \text{Discount Rate} = \frac{110}{499.99} \times 100 \approx 0.220004 \times 100 = 22.00\% \]This tells us that the discount is approximately 22 percent of the regular price.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of mathematics. In this exercise, we particularly deal with subtraction, division, and multiplication.
First, we used subtraction to find the discount amount:

• 499.99 - 389.99 = 110

Next, we did a division to find what portion the discount is of the regular price:

• 110 ÷ 499.99 ≈ 0.220004

Finally, we multiplied by 100 to convert this decimal to a percentage:

• 0.220004 × 100 = 22.00

Each of these steps builds on basic arithmetic.

Rounding Numbers

Rounding numbers is the process of simplifying a number while keeping its value close to what it was. This is useful in making the numbers easier to work with or understand.
Here, we calculated a discount rate of 22.00%. In some contexts, it’s more practical to use whole numbers.
Let's look closer:

• 22.00% is already a whole number, but if we had something like 22.49%, we would look at the tenths place to decide.

RULE: If the digit is 5 or greater, round up. If it’s less than 5, round down.
Examples:

• 22.49% rounds down to 22%
• 22.50% would round up to 23%

Following this rule makes our final discount rate a clean 22%.