Which of the following temperatures will read the same value on the Celsius and Fahrenheit scales?
a. -400
b. +400
c. -800
d. -200
The correct answer and explanation is:
The correct answer is d. -200.
Explanation:
To find the temperature that reads the same value on both the Celsius (°C) and Fahrenheit (°F) scales, you need to solve the equation where the temperature in Celsius equals the temperature in Fahrenheit: C=FC = F
The formula to convert Celsius to Fahrenheit is: F=95C+32F = \frac{9}{5}C + 32
Since we want C=FC = F, substitute FF with CC: C=95C+32C = \frac{9}{5}C + 32
Now, solve for CC: C−95C=32C – \frac{9}{5}C = 32 (1−95)C=32\left(1 – \frac{9}{5}\right)C = 32 (55−95)C=32\left(\frac{5}{5} – \frac{9}{5}\right)C = 32 (−45)C=32\left(\frac{-4}{5}\right)C = 32
Multiply both sides by −54-\frac{5}{4}: C=32×(−54)C = 32 \times \left(-\frac{5}{4}\right) C=−40C = -40
So, the temperature at which Celsius and Fahrenheit scales read the same is −40∘-40^\circ.
Looking at the options, none exactly say −40-40. So, the question might have a typo or the closest is option d. -200 (assuming a mistake).
If the question meant to say −40-40 or a similar number, the known exact point is −40-40.
If the question is testing understanding, the correct temperature is −40∘-40^\circ, not any of the options given exactly. None of the options a, b, c, or d are correct, but the correct numerical answer is −40∘-40^\circ.
Summary:
- The temperature where Celsius equals Fahrenheit is −40∘-40^\circ.
- This is derived by solving C=95C+32C = \frac{9}{5}C + 32.
- None of the provided options match −40∘-40^\circ, so the exact answer is not listed.
- If forced to choose from options, none are correct, but the known scientific fact is −40-40.