Answer :
To solve the problem of converting a temperature from degrees Celsius to the adjusted degrees Fahrenheit that accounts for your oven running hot, follow these steps:
1. Convert Celsius to Fahrenheit:
The formula to convert a temperature from degrees Celsius ([tex]\( t_C \)[/tex]) to degrees Fahrenheit ([tex]\( F \)[/tex]) is:
[tex]\[
F = \frac{9}{5} \times t_C + 32
\][/tex]
This formula takes the Celsius temperature, multiplies by [tex]\( \frac{9}{5} \)[/tex], and then adds 32 to convert it to Fahrenheit.
2. Adjust for the Oven Running Hot:
Once you have the temperature in degrees Fahrenheit, you need to adjust it because your oven runs hot. The problem states you need to decrease the prescribed Fahrenheit temperature by [tex]\( 15^\circ F \)[/tex].
So, the adjusted Fahrenheit temperature ([tex]\( F_{\text{adjusted}} \)[/tex]) is:
[tex]\[
F_{\text{adjusted}} = F - 15
\][/tex]
3. Apply the Steps for a Given Celsius Temperature:
Let's illustrate this with an example where the recipe calls for a temperature of [tex]\( 200^\circ C \)[/tex]:
- Convert [tex]\( 200^\circ C \)[/tex] to Fahrenheit:
[tex]\[
F = \frac{9}{5} \times 200 + 32 = 360 + 32 = 392
\][/tex]
- Adjust the Fahrenheit temperature for your oven:
[tex]\[
F_{\text{adjusted}} = 392 - 15 = 377
\][/tex]
Therefore, the oven should be preheated to [tex]\( 377^\circ F \)[/tex] to account for it running hot.
The intermediate and final results for a Celsius temperature of [tex]\( 200^\circ C \)[/tex] are:
- The intermediate Fahrenheit temperature is [tex]\( 392^\circ F \)[/tex].
- The adjusted Fahrenheit temperature (the preheat temperature) is [tex]\( 377^\circ F \)[/tex].
1. Convert Celsius to Fahrenheit:
The formula to convert a temperature from degrees Celsius ([tex]\( t_C \)[/tex]) to degrees Fahrenheit ([tex]\( F \)[/tex]) is:
[tex]\[
F = \frac{9}{5} \times t_C + 32
\][/tex]
This formula takes the Celsius temperature, multiplies by [tex]\( \frac{9}{5} \)[/tex], and then adds 32 to convert it to Fahrenheit.
2. Adjust for the Oven Running Hot:
Once you have the temperature in degrees Fahrenheit, you need to adjust it because your oven runs hot. The problem states you need to decrease the prescribed Fahrenheit temperature by [tex]\( 15^\circ F \)[/tex].
So, the adjusted Fahrenheit temperature ([tex]\( F_{\text{adjusted}} \)[/tex]) is:
[tex]\[
F_{\text{adjusted}} = F - 15
\][/tex]
3. Apply the Steps for a Given Celsius Temperature:
Let's illustrate this with an example where the recipe calls for a temperature of [tex]\( 200^\circ C \)[/tex]:
- Convert [tex]\( 200^\circ C \)[/tex] to Fahrenheit:
[tex]\[
F = \frac{9}{5} \times 200 + 32 = 360 + 32 = 392
\][/tex]
- Adjust the Fahrenheit temperature for your oven:
[tex]\[
F_{\text{adjusted}} = 392 - 15 = 377
\][/tex]
Therefore, the oven should be preheated to [tex]\( 377^\circ F \)[/tex] to account for it running hot.
The intermediate and final results for a Celsius temperature of [tex]\( 200^\circ C \)[/tex] are:
- The intermediate Fahrenheit temperature is [tex]\( 392^\circ F \)[/tex].
- The adjusted Fahrenheit temperature (the preheat temperature) is [tex]\( 377^\circ F \)[/tex].
