The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation `9C = 5F - 160^(@)`. If the temperature is `10^(@)C`, then what is the temperature in Fahrenheit and if the temperature is `11.75^(@)F`, then what is the temperature in Celsius?

Options

A. `50^(@)F, 11.25^(@)C`
B. `25^(@)F, -17.78^(@)C`
C. `50^(@)F, -11.25^(@)C`
D. `50^(@)F, -17.78^(@)C`

Answer

To solve the problem step by step, we will break it down into two parts: converting Celsius to Fahrenheit and then converting Fahrenheit to Celsius.

### Part 1: Convert 10°C to Fahrenheit

1. **Start with the given equation**:
\[ 9C = 5F - 160 \]
Here, \(C\) is the temperature in Celsius and \(F\) is the temperature in Fahrenheit.

2. **Substitute \(C = 10\)** into the equation:
\[ 9(10) = 5F - 160 \]

3. **Calculate \(9 \times 10\)**:
\[ 90 = 5F - 160 \]

4. **Add 160 to both sides** to isolate the term with \(F\):
\[ 90 + 160 = 5F \]
\[ 250 = 5F \]

5. **Divide both sides by 5** to solve for \(F\):
\[ F = \frac{250}{5} = 50 \]

So, the temperature in Fahrenheit when it is 10°C is **50°F**.

### Part 2: Convert 11.75°F to Celsius

1. **Use the same equation**:
\[ 9C = 5F - 160 \]

2. **Substitute \(F = 11.75\)** into the equation:
\[ 9C = 5(11.75) - 160 \]

3. **Calculate \(5 \times 11.75\)**:
\[ 9C = 58.75 - 160 \]

4. **Subtract 160 from 58.75**:
\[ 9C = 58.75 - 160 = -101.25 \]

5. **Divide both sides by 9** to solve for \(C\):
\[ C = \frac{-101.25}{9} \]
\[ C = -11.25 \]

So, the temperature in Celsius when it is 11.75°F is **-11.25°C**.

### Summary of Results
- 10°C is equivalent to **50°F**.
- 11.75°F is equivalent to **-11.25°C**.