Olivia uses the work below to determine 55% of 720.

Question

Step 1: 55 percent = 50 percent + 10 percent minus one-half (10 percent)
Step 2: 50% of 720 = 720 divided by 2 = 360
10% of 720 = 720 divided by 10 = 72
One-half (10 percent of 720) = One-half (72) = 31
Step 3: 360 + 72 – 31 = 401

Which explains the error in Olivia’s solution?
Step 1: Olivia used percents that are not equivalent to 55%.
Step 2: Olivia incorrectly determined 50% of 720.
Step 2: Olivia incorrectly determined One-half of 10% of 720.
Step 3: Olivia subtracted One-half of 10% when she should have added.

Answer 1

The error in Olivia’s solution lies in Step 1. She claims that 55 percent is equal to 50 percent plus 10 percent minus one-half (10 percent). This can be misleading, as 55% should directly be calculated as 55% rather than breaking it down incorrectly.

The proper breakdown should not involve subtracting one-half of 10% because that would not correctly represent 55%. Therefore, the correct response would be:

Step 1: Olivia used percents that are not equivalent to 55%.

This is the fundamental error in her reasoning, leading to an incorrect total.