Question

A game console that lists for \(\$ 159.95\) is on sale at a discount of \(15 \%\). If there is a \(5 \frac{1}{4} \%\) sales tax, how much will Jane pay for the console? (Round up to a whole cent.) A. \(\$ 143.10\) B. \(\$ 168.35\) C. \(\$ 180.20\) D. \(\$ 183.94\)

Short answer

Jane will pay \(\text{\$143.10}\).

Step-by-step solution

Calculate the discount amount

The discount on the console is 15%. To find the discount amount, multiply the original price by 0.15. Formula: Discount Amount = Original Price × Discount Rate Calculation: Discount Amount = 159.95 × 0.15 = 23.9925

Find the sale price after discount

Subtract the discount amount from the original price to find the sale price. Formula: Sale Price = Original Price - Discount Amount Calculation: Sale Price = 159.95 - 23.9925 ≈ 135.96

Calculate the sales tax amount

The sales tax is 5.25%. To find the sales tax amount, multiply the sale price by 0.0525. Formula: Sales Tax Amount = Sale Price × Sales Tax Rate Calculation: Sales Tax Amount = 135.96 × 0.0525 ≈ 7.1334

Calculate the total price Jane will pay

Add the sales tax amount to the sale price to get the total amount Jane will pay. Round up to the nearest cent. Formula: Total Price = Sale Price + Sales Tax Amount Calculation: Total Price = 135.96 + 7.1334 ≈ 143.10

Key concepts

percentage discount

When shopping, it's common to see items offered at a discounted price. The percentage discount tells us how much we save from the original price. To find out the discount amount, multiply the original price by the discount rate. For example, a game console costing \(\$ 159.95\) on sale at a \(15\%\text{ discount}\) means you save \(\$ 159.95 \times 0.15\). This calculation is quite simple and saves you money. Always remember, the discount amount is subtracted from the original price to find the sale price, which is what you’ll actually pay before any additional taxes or fees.

sales tax calculation

Sales tax is an extra amount we pay on top of the sale price of an item. It's usually a small percentage added by the government. To calculate it, we multiply the sale price by the sales tax rate. For instance, if the sale price of our game console is \(\$ 135.96\) and the sales tax rate is \(5.25\%\), we find the tax amount by \(135.96 \times 0.0525\). Adding this tax to the sale price gives us the total price. It's important to be aware of the sales tax because it directly affects how much money you need to pay at the checkout.

word problem solving

Solving word problems involves understanding the problem, identifying what is asked, and using the correct operations to find the solution. In the given example, we need to find the final price Jane will pay for a game console with a discount and sales tax included. We follow several steps:

• Calculate the discount amount
• Subtract it from the original price to find the sale price
• Calculate the sales tax based on the sale price
• Add the sales tax to the sale price for the total amount

By carefully reading the problem and following these steps, you can solve similar problems with ease.