Question

If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

Answer 1

The number of degrees the temperature extremes differ on the Celsius sale 25 °

Step-by-step explanation:

Here we have

9 °C = 5(F-32)

On the day the temperature extremes recorded at the weather station differed by 45 ° F we then have

F₂ - F₁ = 45

F₂ = F₁ + 45

C₁ = 5(F₁-32)/9

C₂ = 5(F₂-32)/9

C₂ - C₁ = 5(F₂-32)/9 - 5(F₁-32)/9 = 5(F₂ - F₁)/9 = 5×45/9 = 25

Therefore, the number of degrees the temperature extremes differ on the Celsius sale = 25 °

That is the temperature on the Celsius scale increased by 25 °.

Answer 2

The temperature differs in 25 degrees on the Celsius scale

Step-by-step explanation:

The relationship between temperatures on the two scales is:

`9C = 5(F - 32)`

So, if the temperature recorded differed by 45, then the degrees on the Celsius scale can be calculated as follows:

`F_(1) = (9)/(5)(C_(1) + 32)`

`F_(2) = (9)/(5)(C_(2) + 32)`

Since F₂ - F₁ = 45, we have:

`45 = (9)/(5)(C_(2) + 32) - (9)/(5)(C_(1) + 32)`

`45 = (9)/(5)(C_(2) - C_(1) + 32 - 32)`

`45*(5)/(9) = C_(2) - C_(1)`

`C_(2) - C_(1) = 25`

Therefore, the temperature extremes differ in 25 degrees on the Celsius scale.

I hope it helps you!