Question

solve the following word problem. then look at the work. try to determine where the mistake was made. after the start of a new year, a $2,560 television set was marked down to $2,048. what was the percent decrease in the price? given answer: 25% what error is present in this calculation? a) the incorrect operation is performed. b) operations are performed in an incorrect c) the work is incomplete and missing a ste d) a percentage is converted incorrectly.

Explanation:

Step1: Recall percent decrease formula

The formula for percent decrease is $\text{Percent Decrease}=\frac{\text{Original Price}-\text{New Price}}{\text{Original Price}}\times 100\%$.

Step2: Calculate the decrease amount

Original price = $\$2560$, New price = $\$2048$. Decrease amount = $2560 - 2048 = 512$.

Step3: Calculate percent decrease

Using the formula, $\text{Percent Decrease}=\frac{512}{2560}\times 100\%=\frac{512\times100\%}{2560}= 20\%$. The given answer is $25\%$, which means the incorrect operation (maybe using wrong numbers or wrong formula application) was performed. Let's check the options: Option A says incorrect operation is performed. Let's analyze other options: Option B is about order of operations, not relevant here. Option C: The work to get 25% likely has an incorrect operation (like using 2048 as original or miscalculating the decrease), not incomplete. Option D: Conversion is not the issue here as the error is in the operation (calculation of the percent). So the mistake is incorrect operation performed.

Answer:

A) The incorrect operation is performed.