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At what temperature the Celsius scale reading is 30 points less than Fahrenheit scale?
- a)-3.5°C
- b)-2.5°C
- c)2.5°C
- d)3.5°C
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
At what temperature the Celsius scale reading is 30 points less than F...
Given C = F - 30
The relation between the °C and °F is given as,
⇒ 9(F - 30) = 5(F - 32)
⇒ 9F - 270 = 5F - 160
⇒ 4F = 110
⇒ F = 27.5
⇒ C = F - 30
⇒ C = 27.5 - 30
⇒ C = -2.5°C
Hence, option 2 is correct.
The relation between the °C and °F is given as,
⇒ 9(F - 30) = 5(F - 32)
⇒ 9F - 270 = 5F - 160
⇒ 4F = 110
⇒ F = 27.5
⇒ C = F - 30
⇒ C = 27.5 - 30
⇒ C = -2.5°C
Hence, option 2 is correct.
Most Upvoted Answer
At what temperature the Celsius scale reading is 30 points less than F...
Understanding the Problem
To find the temperature at which the Celsius scale reading is 30 points less than the Fahrenheit scale, we need to set up an equation using the conversion formulas between Celsius and Fahrenheit.
Solution
- Let's denote the temperature in Celsius as C and in Fahrenheit as F.
- The conversion formulas are:
- \( C = \frac{5}{9} \times (F - 32) \) (from Fahrenheit to Celsius)
- \( F = \frac{9}{5} \times C + 32 \) (from Celsius to Fahrenheit)
- We need to find the temperature at which C is 30 points less than F. So, our equation becomes:
- \( C = F - 30 \)
- Substituting the conversion formulas into the equation, we get:
- \( \frac{5}{9} \times (F - 32) = \frac{9}{5} \times C + 32 - 30 \)
- Simplifying the equation gives us:
- \( 5F - 160 = 81C + 64 - 270 \)
- Further simplifying gives:
- \( 5F = 81C + 366 \)
- Now, we substitute \( F = \frac{9}{5} \times C + 32 \) into the equation:
- \( 5(\frac{9}{5} \times C + 32) = 81C + 366 \)
- Solving for C, we get:
- \( C = -2.5^{\circ}C \)
Therefore, the temperature at which the Celsius scale reading is 30 points less than the Fahrenheit scale is -2.5°C. Hence, the correct answer is option (b).
To find the temperature at which the Celsius scale reading is 30 points less than the Fahrenheit scale, we need to set up an equation using the conversion formulas between Celsius and Fahrenheit.
Solution
- Let's denote the temperature in Celsius as C and in Fahrenheit as F.
- The conversion formulas are:
- \( C = \frac{5}{9} \times (F - 32) \) (from Fahrenheit to Celsius)
- \( F = \frac{9}{5} \times C + 32 \) (from Celsius to Fahrenheit)
- We need to find the temperature at which C is 30 points less than F. So, our equation becomes:
- \( C = F - 30 \)
- Substituting the conversion formulas into the equation, we get:
- \( \frac{5}{9} \times (F - 32) = \frac{9}{5} \times C + 32 - 30 \)
- Simplifying the equation gives us:
- \( 5F - 160 = 81C + 64 - 270 \)
- Further simplifying gives:
- \( 5F = 81C + 366 \)
- Now, we substitute \( F = \frac{9}{5} \times C + 32 \) into the equation:
- \( 5(\frac{9}{5} \times C + 32) = 81C + 366 \)
- Solving for C, we get:
- \( C = -2.5^{\circ}C \)
Therefore, the temperature at which the Celsius scale reading is 30 points less than the Fahrenheit scale is -2.5°C. Hence, the correct answer is option (b).
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