Problem 147
Question
Nikki bought a patio set on sale for \(\$ 480\). The original price was \(\$ 850\). To the nearest tenth of a percent, what was the rate of discount?
Step-by-Step Solution
Verified Answer
43.5%
1Step 1 - Determine the Amount Saved
Subtract the sale price from the original price to find the amount saved: \(850 - 480 = 370\). So, Nikki saved \(\$370\).
2Step 2 - Calculate the Discount Rate
Use the formula for the discount rate: \[Discount Rate = \left( \frac{Amount \ Saved}{Original \ Price} \right) \times 100 \]. Substitute the values into the formula: \[Discount Rate = \left( \frac{370}{850} \right) \times 100 = 43.52941176\].
3Step 3 - Round to the Nearest Tenth
Round 43.52941176 to the nearest tenth of a percent: 43.5%
Key Concepts
savings calculationdiscount rate formulapercent rounding
savings calculation
Understanding how to calculate savings is a useful skill. In this scenario, Nikki bought a patio set on sale. The initial thing you need to determine is the total amount saved. This is done by subtracting the sale price from the original price.
For Nikki, the original patio set price was \$850\ and she bought it for \$480\. Subtraction gives us:
\[850 - 480 = 370\]
Thus, Nikki saved \$370\ on her purchase.
Knowing how to find the savings amount helps in further calculations, like finding out the discount rate.
Remember to always subtract the sale price from the original price to get the correct savings.
For Nikki, the original patio set price was \$850\ and she bought it for \$480\. Subtraction gives us:
\[850 - 480 = 370\]
Thus, Nikki saved \$370\ on her purchase.
Knowing how to find the savings amount helps in further calculations, like finding out the discount rate.
Remember to always subtract the sale price from the original price to get the correct savings.
discount rate formula
The discount rate formula is key when you want to understand how much of a discount you received. After calculating the savings, you can determine the discount rate using the following formula:
\[Discount \,Rate = \left(\frac{Amount \,Saved}{Original \,Price}\right) \times 100\]
Using Nikki's example, we substitute the values:
\[Discount \,Rate = \left(\frac{370}{850}\right) \times 100 = 43.52941176\]
This shows that Nikki received a discount rate of approximately 43.5%.
Understanding this formula allows you to compare discounts on different items easily. Simply remember to divide the amount saved by the original price and multiply by 100 to find the percentage.
\[Discount \,Rate = \left(\frac{Amount \,Saved}{Original \,Price}\right) \times 100\]
Using Nikki's example, we substitute the values:
- Amount Saved: \$370\
- Original Price: \$850\
\[Discount \,Rate = \left(\frac{370}{850}\right) \times 100 = 43.52941176\]
This shows that Nikki received a discount rate of approximately 43.5%.
Understanding this formula allows you to compare discounts on different items easily. Simply remember to divide the amount saved by the original price and multiply by 100 to find the percentage.
percent rounding
Rounding percentages helps present data more clearly. In many cases, you may need to round to the nearest tenth for simplicity.
For Nikki's discount rate, we first calculated it to be 43.52941176%. To round this number to the nearest tenth, we look at the digit in the hundredths place.
If the digit in the hundredths place is less than 5, you round down, and if it's 5 or more, you round up. In this example:
\[43.52941176\] is rounded to \[43.5\]%, because the hundredths place digit (2) is less than 5.
Therefore, the discount rate rounded to the nearest tenth of a percent is 43.5%.
Rounding makes numbers easier to understand and more practical for everyday use. So, always check the next digit to decide whether to round up or down accordingly.
For Nikki's discount rate, we first calculated it to be 43.52941176%. To round this number to the nearest tenth, we look at the digit in the hundredths place.
If the digit in the hundredths place is less than 5, you round down, and if it's 5 or more, you round up. In this example:
\[43.52941176\] is rounded to \[43.5\]%, because the hundredths place digit (2) is less than 5.
Therefore, the discount rate rounded to the nearest tenth of a percent is 43.5%.
Rounding makes numbers easier to understand and more practical for everyday use. So, always check the next digit to decide whether to round up or down accordingly.
Other exercises in this chapter
Problem 137
Angelo's store is having a sale on televisions. One television, with original price \(\$ 859,\) is selling for \(\$ 125\) off.
View solution Problem 141
Erys bought a treadmill on sale at \(35 \%\) off. The original price was \(\$ 949.95\) (round to the nearest cent.)
View solution Problem 148
Stella bought a dinette set on sale for \(\$ 725\). The original price was \(\$ 1,299 .\) To the nearest tenth of a percent, what was the rate of discount?
View solution Problem 155
Leaving a Tip At the campus coffee cart, a medium coffee costs \$1.65. MaryAnne brings \(\$ 2.00\) with her when she buys a cup of coffee and leaves the change
View solution