Question

The same front hit Pittsburgh the next morning. The temperature dropped by 8°F each hour from 5:00 a.M. To 9:00 a.M.. If the temperature at 9:00 a.M. Was -5°F what was the beginning temperature at 5:00 a.M.? There are different ways to solve a problem. Claire and Dan solved this problem differently. Dan said his method involved multiplication, while Claire said she did not use multiplication. Both students arrived at the correct answer. How is this possible? Explain. What answer did they both arrive at?

Answer 1

The beginning temperature at 5:00 a.M was 27°F

The answer they both arrived at was 27°F

Explanation:

From the question,

The temperature dropped by 8°F each hour from 5:00 a.M. To 9:00 a.M.

From 5:00 a.M to 9:00 a.M, there are 4 hours.

Hence, the temperature dropped by 8°F each hour for 4 hours.

Also, from the question

The temperature at 9:00 a.M. was -5°F,

To determine the beginning temperature at 5:00 a.M,

Let the beginning temperature be x

For Dan's method, his method involved multiplication, He could have done it this way:

Since the temperature dropped by 8°F each hour for 4 hours,

This means the temperature would have reduced by 4 × 8°F = 32°F

Now, we can write that

x - 32°F = -5°F

Then, x = -5°F + 32°F

x = 27°F

For Claire's method, she did not use multiplication, she could have done it step-wisely, reducing the temperature by 8°F every hour.

Since the temperature dropped by 8°F each hour from 5:00 a.M. To 9:00 a.M,

Let the beginning temperature be x

After 1 hour, that is at 6:00 a.M, the temperature will be x - 8°F

After 2 hours, that is at 7:00 a.M, the temperature will be x - 8°F - 8°F = x -16°F

After 3 hours, that is at 8:00 a.M, the temperature will be x -16°F - 8°F = x -24°F

After 4 hours, that is at 9:00 a.M, the temperature will be x -24°F - 8°F = x -32°F

From the question, the temperature at 9:00 a.M. was -5°F

Hence,

x -32°F = -5°F

Then,

x = -5°F + 32°F

x = 27°F

Hence, the answer they both arrived at was 27°F.