Problem 70 - Elementary Algebra

Question

The original price of a backpack carrier for dogs that weigh up to 22 pounds is \(\$ 69.97\). On sale, it is \(\$ 39.95\). Find the percent discount. Round to the nearest percent.

Step-by-Step Solution

Answer

43%

Step 1 - Find the Difference in Price

To find the difference between the original price and the sale price, subtract the sale price from the original price. Original Price: \( \$69.97 \) Sale Price: \( \$39.95 \) Difference: \( \$69.97 - \$39.95 = \$30.02 \)

Step 2 - Calculate the Discount Percent

To find the percent discount, divide the difference by the original price and multiply by 100. Percent Discount: \[\left( \frac{\$30.02}{\$69.97} \right) * 100 = 42.9\%\]

Step 3 - Round to the Nearest Percent

Round the percent discount to the nearest whole number. \( 42.9\% \approx 43\% \)

Key Concepts

difference in price

Understanding the difference in price is the first step in calculating a percent discount. In this exercise, the original price of the backpack carrier is \(\$69.97\), and the sale price is \(\$39.95\). To find the difference, subtract the sale price from the original price.

\(\$69.97 - \$39.95 = \$30.02\).

This \(\$30.02\) represents how much you save by purchasing the item on sale. Visualizing this first step helps understand the amount saved before moving to the percent calculation.

calculate discount

Once the difference in price is known, the next step is to calculate the discount percent. This involves dividing the difference by the original price and then multiplying by 100.

The formula used here is:
\(\text{Percent Discount} = \left( \frac{\$30.02}{\$69.97} \right) * 100 = 42.9\%\).

Breaking it down:

• Divide \(\$30.02\) by the original price \(\$69.97\).
• Result: 0.429
• Multiply the result by 100 to convert it to a percentage: 42.9%

This gives the discount percentage before rounding.

rounding percentages

The final step involves rounding the calculated percent discount to the nearest whole number.

In this case, 42.9% is close to 43%.

When rounding percentages:

• If it's 0.5 or above, round up.
• If it's below 0.5, round down.

So, 42.9% rounds to 43%. Hence, the rounded discount percentage is 43%.
This step ensures that the percent discount is simple and easy to understand.