Question

$$C=5/9(F-32)$$

The equation above shows how temperature $F$, measured in degrees Fahrenheit, relates to a temperature $C$, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $5/9$ degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of $5/9$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

Answer 1

Answer on Question #79051 – Math – Algebra

My answer is D) I and II only.

Indeed. Consider all three cases.

1) C - ? if F + 1

C = 5/9 * (F - 32) = 5/9 * F - 160/9

C + x = 5/9 * (F + 1) - 160/9

5/9 * F - 160/9 + x = 5/9 * (F + 1) - 160/9

5F - 160 + 9x = 5F - 155

9x = 5

x = 5/9

So we can see that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $5/9$ degree Celsius – it’s true

2) F - ? if C + 1

C = 5/9 * (F - 32)

5/9 * F = C + 160/9

5F = 9C + 160

F = 9/5 C + 32

F + x = 9/5 * (C + 1) + 32

9/5 * C + 32 + x = 9/5 * C + 9/5 + 32

x = 9/5

x = 1.8

Thus, in this case we see that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit – it’s true

3) And in the end we’ll check the third statement: A temperature increase of $5/9$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

C - ? if F + 5/9

C = 5/9 * (F - 32)

C + x = 5/9 * (F + 5/9 - 32)

5/9 * (F - 32) + x = 5/9 * (F + 5/9 - 32)

5F - 160 + 9x = 5F + 25 - 160

x = 25/9,

so the statement is false.

Answer: D) I and II only.

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