Final answer:
After calculating the pre-tax price of the backpack by dividing the total cost by 1.06, and then calculating the sales tax, we find that the backpack costs $31.01 after tax. Thus, spending $33 on a backpack that costs $31 including tax is not reasonable.
Step-by-step explanation:
If the sales tax in New Jersey is 6% and a backpack costs $31 including tax, it is reasonable to determine if spending $33 on the backpack is justified. The challenge is finding the original price without tax and then adding the appropriate tax to see if it equals $33.
Firstly, to calculate sales tax as a monetary value, convert the percentage to a decimal and multiply by the item's pre-tax cost. However, in this case, we have the final price with tax, which is $31. To find the pre-tax cost, we divide the final price by 1 plus the tax rate (in decimal form). That would be $31 / 1.06 = approximately $29.25.
Then, to find the amount of sales tax on the original price, multiply the original price by the tax rate. For this example, $29.25 × 0.06 = about $1.755. However, we need to round $1.755 to the nearest penny which would be $1.76.
Adding the original price of $29.25 and the sales tax of $1.76 gives us a total cost of $31.01, which is what we would expect after including tax. Spending $33 on a backpack that costs $31, including tax, seems unreasonable. Therefore, the correct answer is B) No, it is not reasonable to spend $33.