A store advertises 25% off a $33 shirt. What is the sale price
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A store advertises 25% off a 33 dollar shirt. What is the sale price? Let's break down what this means. We have a shirt originally priced at 33 dollars, and the store is offering a 25 percent discount. This means the customer will pay less than the original price. Our goal is to calculate the final sale price after applying this discount.
There are two common methods to solve percentage discount problems. Method one: Calculate the discount amount first, then subtract it from the original price. For our example, we would calculate 25 percent of 33 dollars, which is 8 dollars and 25 cents, then subtract that from 33 dollars to get the sale price. Method two: Calculate what percentage you actually pay, then multiply. Since we're getting 25 percent off, we're paying 75 percent of the original price. So we multiply 33 dollars by 0.75. Both methods will give us the same result, but one might be more intuitive depending on the situation.
Let's work through method one step by step. Step one: Convert 25 percent to a decimal. To do this, we divide by 100, so 25 percent equals 0.25. Step two: Calculate the discount amount by multiplying the original price by this decimal. That's 33 dollars times 0.25, which equals 8 dollars and 25 cents. Step three: Subtract the discount amount from the original price. So we calculate 33 dollars minus 8 dollars and 25 cents, which gives us 24 dollars and 75 cents. This is our final sale price.
Now let's look at method two, which is often more direct. If 25 percent is taken off, that means you pay 75 percent of the original price. Step one: Calculate the percentage you actually pay. We subtract the discount from 100 percent, so 100 percent minus 25 percent equals 75 percent. Step two: Convert this percentage to a decimal by dividing by 100. So 75 percent equals 0.75. Step three: Multiply the original price by this decimal. That's 33 dollars times 0.75, which equals 24 dollars and 75 cents. This is the same result we got with method one, but with one fewer step.
Both methods give us the same result: 24 dollars and 75 cents. Let's verify this is correct by adding the discount amount back to the sale price. 24 dollars and 75 cents plus 8 dollars and 25 cents equals 33 dollars, which is our original price. This confirms our answer is correct. Now let's compare the two methods. Method one is more intuitive for some people because it clearly shows the discount amount. This can be helpful when you want to know exactly how much you're saving. Method two is more direct because it calculates the final price in one step rather than two. This can be faster, especially when doing mental math. Both methods are mathematically equivalent, so you can choose the one that feels more comfortable for you.
Let's practice with two more examples to reinforce our understanding. Example one: A 40 dollar item with 30 percent off. Using method one, we first calculate the discount amount. 40 dollars times 0.30 equals 12 dollars. Then we subtract that from the original price. 40 dollars minus 12 dollars equals 28 dollars. Using method two, we calculate what percentage we pay. 100 percent minus 30 percent equals 70 percent, or 0.70 as a decimal. Then we multiply. 40 dollars times 0.70 equals 28 dollars. Both methods give us the same sale price of 28 dollars. Example two: A 25 dollar item with 15 percent off. Method one: Calculate the discount. 25 dollars times 0.15 equals 3 dollars and 75 cents. Subtract from the original price. 25 dollars minus 3 dollars and 75 cents equals 21 dollars and 25 cents. Method two: Calculate percentage paid. 100 percent minus 15 percent equals 85 percent, or 0.85 as a decimal. Multiply. 25 dollars times 0.85 equals 21 dollars and 25 cents. Again, both methods give the same result.
Understanding how to calculate percentage discounts has many practical applications in real-world shopping scenarios. Seasonal sales like Black Friday or end-of-season clearance events often offer significant percentage discounts. Store promotions and coupons provide another common way to save money through percentage reductions. When buying in bulk, you might receive discounts for purchasing larger quantities. Many stores have loyalty programs that offer members special percentage discounts or rewards. Finally, flash sales and limited-time offers create urgency with temporary percentage discounts. By mastering these calculations, you can make more informed purchasing decisions, compare deals effectively, and budget your spending more accurately. This mathematical skill helps you become a smarter consumer in our everyday shopping experiences.