A discount is a percent decrease from the original price.
You can find the discount amount first and subtract it from the original price.
You can also multiply the original price by the discount written as a decimal.
Another efficient strategy is to find the percent that remains after the discount.
When money is involved, answers are usually written to the nearest cent.
✏️ Worked Examples
Strategy 1: Use a Proportion
A backpack has a retail price of 💲 \(\displaystyle 64\). A store offers a 25% discount. How much will the customer pay after the discount?
First, find the discount amount with a proportion.
\(\displaystyle \frac{25}{100}=\frac{d}{64}\)
Cross multiply.
\(\displaystyle 100d=1600\)
\(\displaystyle d=16\)
The discount is 💲 \(\displaystyle 16\).
Subtract the discount from the original price.
\(\displaystyle 64-16=48\)
The customer will pay 💲 \(\displaystyle 48\).
Strategy 2: Multiply by the Decimal Discount
Use the same problem.
A backpack has a retail price of 💲 \(\displaystyle 64\). A store offers a 25% discount. How much will the customer pay after the discount?
Write the discount percent as a decimal.
\(\displaystyle 25\%=0.25\)
Multiply to find the discount amount.
\(\displaystyle 64\times0.25=16\)
Subtract the discount from the original price.
\(\displaystyle 64-16=48\)
The customer will pay 💲 \(\displaystyle 48\). This method is often quicker because it goes straight from percent to discount amount.
Strategy 3: Find the Percent You Still Pay
Use the same problem again.
A backpack has a retail price of 💲 \(\displaystyle 64\). A store offers a 25% discount. How much will the customer pay after the discount?
Instead of finding the discount first, find the percent that remains.
\(\displaystyle 100\%-25\%=75\%\)
Write \(\displaystyle 75\%\) as a decimal.
\(\displaystyle 75\%=0.75\)
Multiply by the original price.
\(\displaystyle 64\times0.75=48\)
The customer will pay 💲 \(\displaystyle 48\). This strategy is efficient because it finds the sale price directly.
🧠 Math Vocabulary
Original Price: the starting price before a discount is applied.
Discount: the amount or percent taken off the original price.
Sale Price: the amount paid after the discount.
Percent Decrease: the percent an amount goes down compared to the original amount.
Coupon: an offer that reduces the price by a certain amount or percent.
💡 Main Idea
Discount problems show how percentages apply to real shopping situations. Students can solve these problems in more than one correct way, including finding the discount amount first or finding the percent that remains after the discount. Seeing multiple strategies helps build flexibility and confidence.
📚 What You Should Already Know
Before solving discount problems, students should know how to convert percentages to decimals, find a percent of a number, and subtract to find the final amount.
🚀 What Comes Next
After learning how to solve discount problems, students can move on to sales tax, markup, markdown, percent increase, and multi-step consumer math applications.
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