What Celsius temperature will the Fahrenheit thermometer be 4-times more than on the Celsius thermometer?
At what Celsius temperature will the numerical reading on the Fahrenheit thermometer be 1/9 that on the Celsius thermometer?
I just need a solution to the first half of the question I figured out the 2nd half
thank you
To answer these questions, we need to understand the relationship between Celsius and Fahrenheit temperatures.
The formula to convert Celsius to Fahrenheit is:
F = (C × 9/5) + 32
Where F is the temperature in Fahrenheit and C is the temperature in Celsius.
Let's use this formula to find the solutions:
1. When the Fahrenheit temperature is 4 times greater than the Celsius temperature:
Let's assume the Celsius temperature is C. According to the given condition, the Fahrenheit temperature will be 4 times greater, so it will be 4C.
Using the formula, we can set up the equation:
4C = (C × 9/5) + 32
Now we can solve for C:
4C = (9C/5) + 32
Multiply both sides by 5:
20C = 9C + 160
Subtract 9C from both sides:
11C = 160
Divide both sides by 11:
C = 14.545
Therefore, the Celsius temperature needed for the Fahrenheit thermometer to be 4 times greater is approximately 14.545 degrees Celsius.
2. When the numerical reading on the Fahrenheit thermometer is 1/9 that on the Celsius thermometer:
Again, let's assume the Celsius temperature is C. According to the given condition, the Fahrenheit temperature will be 1/9 of the Celsius temperature, so it will be (1/9)C.
Using the formula, we can set up the equation:
(1/9)C = (C × 9/5) + 32
Now we can solve for C:
(1/9)C = (9C/5) + 32
Multiply both sides by 9:
C = 9(9C/5) + 288
Simplify:
C = (81C/5) + 288
Multiply both sides by 5:
5C = 81C + 1440
Subtract 81C from both sides:
-76C = 1440
Divide both sides by -76:
C = -18.947
Therefore, the Celsius temperature when the numerical reading on the Fahrenheit thermometer is 1/9 that on the Celsius thermometer is approximately -18.947 degrees Celsius.
(9/5)c + 32 = 4c
Solve for c.