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 128% on her monthly energy bill.

choose the correct answer below.

a. the claim could be true because her new monthly energy bill would be 72% of the previous monthly energy bill, which makes sense.
b. the claim could not be true because her new monthly energy bill would be -72% of the previous monthly energy bill. this is impossible since the bill cannot be negative.
c. the claim could be true because her new monthly energy bill would be 28% of the previous monthly energy bill, which makes sense.
d. the claim could not be true because her new monthly energy bill would be -28% of the previous monthly energy bill. this is impossible since the bill cannot be negative.

Explanation:

Analyze the mathematical meaning of saving 128%

$$ \text{Savings} = 1.28 \times \text{Original Bill} $$

$$ \text{New Bill} = \text{Original Bill} - \text{Savings} = \text{Original Bill} \times (1 - 1.28) = -0.28 \times \text{Original Bill} $$

Evaluate the feasibility of a negative bill

$$ \text{New Bill} = -28\% \text{ of the previous monthly energy bill} $$

An energy bill cannot be negative under normal circumstances (saving more than 100% of the cost is impossible).

Match with the given options

Option D correctly states that the claim could not be true because the new bill would be \(-28\%\) of the previous bill, which is impossible since the bill cannot be negative.

Answer:

• A. The claim could be true because her new monthly energy bill would be 72% of the previous monthly energy bill, which makes sense.
• B. The claim could not be true because her new monthly energy bill would be -72% of the previous monthly energy bill. This is impossible since the bill cannot be negative.
• C. The claim could be true because her new monthly energy bill would be 28% of the previous monthly energy bill, which makes sense.
• D. The claim could not be true because her new monthly energy bill would be -28% of the previous monthly energy bill. This is impossible since the bill cannot be negative. (Correct answer)