At 4 p.m., the temperature started to change drastically. Each hour, for three hours, the temperature decreased by 7°F. Which expression best shows another way to write the product for the temperature change? (A) 7 + 7 + 7 (B) 7 + 7 + 7 + 7 (C) (-1)(7 + 7 + 7) (D) (-7) + (-7) + (-7) + (-7)
Answer (1)
To determine which expression best shows another way to write the product for the temperature change, let's break down the scenario given in the question.
At 4 p.m., the temperature starts decreasing by 7°F each hour for three hours. So, over these three hours, the temperature decreases a total of 3 times by 7°F. Here are the steps to find the right expression:
Analyze the temperature changes each hour. Each hour, the temperature decreases by − 7° F . Hence, for three hours, the temperature will decrease by: − 7 + ( − 7 ) + ( − 7 ) = − 21
The product of multiplying the decrease by the number of hours can be written as: ( − 7 ) × 3
Now, let’s evaluate the provided options:
(A) 7 + 7 + 7 : This represents an increase of 21° F , so it's not correct.
(B) 7 + 7 + 7 + 7 : This signifies an increase of 28° F , which doesn't match the scenario.
(C) ( − 1 ) ( 7 + 7 + 7 ) : This means ( − 1 ) × 21° F = − 21° F , which represents a decrease of 21° F and matches the temperature change described.
(D) ( − 7 ) + ( − 7 ) + ( − 7 ) + ( − 7 ) : This shows four instances of − 7 , representing a decrease of 28° F , which is not the correct total decrease.
Therefore, the correct choice is (C) ( − 1 ) ( 7 + 7 + 7 ) because it accurately represents the total temperature decrease over three hours.
