Question

determine whether the following claim could be true. explain your answer. by turning off her lights and closing her windows at night, maria saved 120% on her monthly energy bill. choose the correct answer below. a. the claim could be true because her new monthly energy bill would be 20% of the previous monthly energy bill, which makes sense. b. the claim could be true because her new monthly energy bill would be 80% of the previous monthly energy bill, which makes sense. c. the claim could not be true because her new monthly energy bill would be −20% of the previous monthly energy bill. this is impossible since the bill cannot be negative. d. the claim could not be true because her new monthly energy bill would be −80% of the previous monthly energy bill. this is impossible since the bill cannot be negative.

Explanation:

To determine if saving 120% on a bill is possible, we analyze the percentage saved. A 100% savings would mean the new bill is $0$ (since $100\%$ of the original bill is the full amount). Saving more than 100%, like 120%, would imply the new bill is $100\% - 120\%=- 20\%$ of the original bill. Since a bill (a cost) cannot be negative (you can't have a negative amount to pay), this is impossible. Now let's check the options:

• Option A: A 120% savings doesn't lead to 20% of the original bill. Incorrect.
• Option B: A 120% savings doesn't lead to 80% of the original bill. Incorrect.
• Option C: Calculating the new bill as $100\% - 120\%=-20\%$ of the original, and since a bill can't be negative, the claim is false. Correct.
• Option D: The calculation for the new bill is wrong (should be -20% not -80%). Incorrect.

Answer:

C. The claim could not be true because her new monthly energy bill would be -20% of the previous monthly energy bill. This is impossible since the bill cannot be negative.