In the Fahrenheit temperature scale, water freezes at 32°F and boils at 212°F. In the Celsius (or centigrade) scale, water freezes at 0°C and boils at 100°C. Assuming that the Fahrenheit temperature F and the Celsius temperature C are related by a linear equation, find the Celsius temperature that correspond to 39°F, to the nearest degree.
A)54°C
B) 7°C
C) 4°C
D) 39°C
E) 38°C

Question

In the Fahrenheit temperature scale, water freezes at 32°F and boils at 212°F. In the Celsius (or centigrade) scale, water freezes at 0°C and boils at 100°C. Assuming that the Fahrenheit temperature F and the Celsius temperature C are related by a linear equation, find the Celsius temperature that correspond to 39°F, to the nearest degree. ​
A)54°C
B) 7°C
C) 4°C
D) 39°C
E) 38°C

Quizplus · Accepted Answer

We know that the relationship between Fahrenheit and Celsius is linear, meaning that it can be represented by an equation of the form C = mF + b, where m and b are constants. To find the values of m and b, we can use the fact that water freezes at 32°F and 0°C, and water boils at 212°F and 100°C:

0 = 32m + b
100 = 212m + b

Subtracting the first equation from the second, we get:

100 = 180m

Solving for m, we find that m = 5/9. Plugging this value of m into either of the two equations, we can solve for b:

0 = 32(5/9) + b
b = -160/9

Therefore, the equation that relates Fahrenheit and Celsius temperatures is:

C = (5/9)F - (160/9)

To find the Celsius temperature that corresponds to 39°F, we can simply plug in F = 39 and solve for C:

C = (5/9)(39) - (160/9) ≈ 3.89 ≈ 4°C (to the nearest degree)

In the Fahrenheit Temperature Scale, Water Freezes at 32°F and Boils