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If C is the temperature in degrees Celsius and F is the temperature in

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If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 21 Sep 2019, 05:53
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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?

A. 65/9
B. 13
C. 25
D. 45
E. 81

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Re: If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 21 Sep 2019, 06:15
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gmatt1476 wrote:
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?

A. 65/9
B. 13
C. 25
D. 45
E. 81

PS23502.01


9C = 5(F – 32)
--> C = 5F/9 - 32/9

Let \(F_1\) & \(F_2\) be the recorded temperatures in Fahrenheit and
\(C_1\) & \(C_2\) be the recorded temperatures in Celsius

--> \(C_1\) = 5\(F_1\)/9 - 32/9 ....... (1)
&
\(C_2\) = 5\(F_2\)/9 - 32/9 ....... (2)

Given, \(F_2\) - \(F_1\) = 45

(2) - (1) --> \(C_2\) - \(C_1\) = 5\(F_2\)/9 - 5\(F_1\)/9 = 5/9*(\(F_2\) - \(F_1\)) = 5/9*45 = 25

IMO Option C

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Re: If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 21 Sep 2019, 06:42
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1
given
C=5/9F-32/9
F1-F2=45
C1=5/9F1-32/9
C2=5/9F1-32/9
subtract
c1-c2= 5/9*45 ; 25
IMO C


gmatt1476 wrote:
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?

A. 65/9
B. 13
C. 25
D. 45
E. 81

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Re: If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 21 Sep 2019, 11:40
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gmatt1476 wrote:
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?

A. 65/9
B. 13
C. 25
D. 45
E. 81

PS23502.01


\(C=\frac{5}{9}F-\frac{160}{9}\)

The slope of the above line is \(\frac{\Delta{C}}{\Delta{F}}=\frac{5}{9}\). Since \(\Delta{F}=45\),

\(\Delta{C}=\frac{5}{9}\cdot 45=25\)

Answer: C
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Re: If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 14 Dec 2019, 17:36
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gmatt1476 wrote:
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?

A. 65/9
B. 13
C. 25
D. 45
E. 81

PS23502.01


To find the answer, let's find the Celsius conversion for two temperatures that differ by 45 degrees, on the Fahrenheit scale.

Start with 32 degrees Fahrenheit
Plug into the formula to get 9C = 5(32 – 32)
Simplify: 9C = 0
Solve: C = 0
So 32 degrees Fahrenheit = 0 degrees Celsius


32 + 45 = 77
So let's convert 77 degrees Fahrenheit into Celsius
Plug into the formula to get 9C = 5(77 – 32)
Simplify: 9C = 5(45)
Divide both sides by 9 to get: C = 5(5) = 25
So 77 degrees Fahrenheit = 25 degrees Celsius

25 - 0 = 25
So, a 45-degree difference in Fahrenheit is equal to a 25-degree difference in Celsius.

Answer: C

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Brent
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Re: If C is the temperature in degrees Celsius and F is the temperature in  [#permalink]

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New post 15 Dec 2019, 14:49
Hi All,

We're told that C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, and 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, we're asked by how many degrees did the temperature extremes differ on the Celsius scale. This question can be solved rather easily by TESTing VALUES (as Brent has shown in his post). In addition, the answer choices are sufficiently 'spread out' that we can use a little logic and a little math to answer this question without too much work.

The equation 9C = 5(F - 32) can be 'rewritten' as...

C = 5(F - 32)/9

5/9 is a little more than 1/2.... so we can 'rewrite' the equation again as....

C = (a little more than 1/2)(F - 32)

Thus, for every degree that F 'changes', the value of C will change by a little more than 1/2 of a degree.

In this question, F changes by 45 degrees, so the value of C will change by (a little more than 1/2)(45) degrees. Half of 45 is 22.5, so we're looking for an answer that's a little more than 22.5 degrees. There's only one answer that matches...

Final Answer:

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Re: If C is the temperature in degrees Celsius and F is the temperature in   [#permalink] 15 Dec 2019, 14:49
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