Question

Preston is looking at a watch that costs \(\$ 9.99\), but he only has \(\$ 10\) to spend. Sales tax is \(6 \%\). How much more money does Preston need in order to purchase the watch? A. \(\$ 0.61\) B. \(\$ 0.60\) C. \(\$ 0.59\) D. \(\$ 0.58\)

Short answer

\$ 0.59

Step-by-step solution

Calculate the sales tax

First, calculate the sales tax for the watch. The sales tax is 6% of the watch's price. Use the formula: \[ \text{Sales tax} = \text{Price} \times \text{Tax rate} \] Substitute the given values: \[ \text{Sales tax} = 9.99 \times 0.06 \] This gives us: \[ \text{Sales tax} = 0.5994 \]

Calculate the total cost

Add the sales tax to the original price of the watch to find the total cost using the formula: \[ \text{Total cost} = \text{Price} + \text{Sales tax} \] Substitute the values: \[ \text{Total cost} = 9.99 + 0.5994 \] This gives us: \[ \text{Total cost} = 10.5894 \]

Determine the shortfall

Subtract the amount of money Preston has from the total cost to find out how much more money he needs using the formula: \[ \text{Shortfall} = \text{Total cost} - \text{Preston's money} \] Substitute the values: \[ \text{Shortfall} = 10.5894 - 10 \] This gives us: \[ \text{Shortfall} = 0.5894 \] Round the result to the nearest cent: \[ \text{Shortfall} \rightarrow 0.59 \]

Key concepts

Percentage Calculation

Understanding percentage calculation is crucial for solving many everyday math problems. Percentages represent a part out of 100. For example, a 6% tax rate means 6 out of every 100 units of the item’s price.

In this exercise, we calculated a 6% sales tax on a watch priced at \( \$9.99 \) using the formula: \[ \text{Sales tax} = \text{Price} \times \text{Tax rate} \] Thus, \[ \text{Sales tax} = 9.99 \times 0.06 = 0.5994 \] Notice we converted 6% to a decimal (0.06) for multiplication. This shows the importance of understanding how to convert percentages to decimals by moving the decimal point two places left.

It’s also useful to round up to common decimal places. Instead of dealing with the lengthy 0.5994, we can round it to 0.60, making mental math quicker and easier.

Sales Tax

Sales tax is a percentage of an item's price added to the price at the point of purchase. It's essential to understand how to calculate sales tax as it affects the total cost. To find the total cost with sales tax, you multiply the price by the tax rate and then add this to the original price.

In our example, after finding the sales tax (0.5994), we add it to the watch's price: \[ \text{Total cost} = \$9.99 + 0.5994 = 10.5894 \] We can round this to \( \$10.59 \), making it easier to handle, especially when dealing with currency.

Always check the exact sales tax rate in your area, as it varies by location. The principles remain the same, and mastering this ensures you never get an unexpected surprise at the checkout counter.

Subtraction

Subtraction is the method used to determine the difference between two numbers. Here, it helps find out how much more money Preston needs.

After calculating the total cost (\( \$10.59 \)), we subtract the amount Preston has: \[ \text{Shortfall} = \text{Total cost} - \text{Preston's money} = 10.59 - 10 = 0.59 \] This tells us Preston needs an additional \( \$0.59 \) to buy the watch.

Subtracting can also be crucial for budgeting and financial planning. It helps ensure you have enough funds before making purchases. Always round your final results to the nearest cent to avoid discrepancies.