- Calculate the discount for each item by multiplying the original price by \(\frac{1}{4}\) (or \(0.25\)).
- Subtract the discount from the original price to find the sale price (\(P - D = S\)).
- The calculated results are:
- Shirt: Discount \(\$4.99\), Sale Price \(\$14.98\)
- Jacket: Discount \(\$24.99\), Sale Price \(\$74.98\)
- Pants: Discount \(\$10.50\), Sale Price \(\$31.50\)
- Socks: Discount \(\$1.15\), Sale Price \(\$3.45\)
- Sweater: Discount \(\$10.00\), Sale Price \(\$29.99\).
- Final Answer Summary: \(\boxed{\text{See item list above}}\)
Explanation
- Problem Analysis and Setup
We need to calculate the discount amount and the final sale price for five items: a shirt, a jacket, pants, two pairs of socks, and a sweater. The original prices are given as: shirt (\$19.97), jacket (\$99.97), pants (\$42.00), socks (\$4.60), and sweater (\$39.99). The discount rate is \(1/4\), which is equivalent to 25% or a multiplier of 0.25. The discount amount \(D\) is calculated as the product of the original price \(P\) and the discount rate: \(D = P \times 0.25\). The sale price \(S\) is then calculated as the difference between the original price and the discount: \(S = P - D = P \times (1 - 0.25) = P \times 0.75\). Note that the expression \(-7 \div 4\) provided in the prompt is extraneous and does not affect the calculation of the discounts.
- Calculation of Discounts and Sale Prices
Now we calculate the values for each item using the formulas \(D = P \times 0.25\) and \(S = P - D\).
- Shirt (\(\$19.97\)):
Discount: \(19.97 \times 0.25 = 4.9925 \approx \$4.99\)
Sale Price: \(19.97 - 4.99 = \$14.98\)
- Jacket (\(\$99.97\)):
Discount: \(99.97 \times 0.25 = 24.9925 \approx \$24.99\)
Sale Price: \(99.97 - 24.99 = \$74.98\)
- Pants (\(\$42.00\)):
Discount: \(42.00 \times 0.25 = \$10.50\)
Sale Price: \(42.00 - 10.50 = \$31.50\)
- Socks (2 pairs) (\(\$4.60\)):
Discount: \(4.60 \times 0.25 = \$1.15\)
Sale Price: \(4.60 - 1.15 = \$3.45\)
- Sweater (\(\$39.99\)):
Discount: \(39.99 \times 0.25 = 9.9975 \approx \$10.00\)
Sale Price: \(39.99 - 10.00 = \$29.99\)
- Final Results
The calculations confirm the discounted values for each of the items. The final summary of the discount amounts and sale prices at a 25% reduction is:
- Shirt: Discount \(\$4.99\), Sale Price \(\$14.98\)
- Jacket: Discount \(\$24.99\), Sale Price \(\$74.98\)
- Pants: Discount \(\$10.50\), Sale Price \(\$31.50\)
- Socks: Discount \(\$1.15\), Sale Price \(\$3.45\)
- Sweater: Discount \(\$10.00\), Sale Price \(\$29.99\)
These values represent the correct application of a \(\frac{1}{4}\) off discount to the original prices provided.
Examples
Understanding how to calculate percentages and discounts is a fundamental life skill, useful for everything from shopping at the grocery store to budgeting for clothing. For example, if you see a favorite brand of headphones on sale for 25% off their original price of \(\$120\), you can quickly determine the savings of \(120 \times 0.25 = \$30\) and the final cost of \(120 - 30 = \$90\). Mastering these simple calculations helps you make smarter financial decisions and ensures you always get the best value for your money.