A solution is to be kept between `50^(@) F and 68^(@)F `. What is the range of temperature in degree celcius if Celcius-farhenheit conversion formual is : `F= (9)/(5) C + 32`

Explanation

To find the range of temperature in degrees Celsius when the solution is kept between 50°F and 68°F, we will use the Celsius-Fahrenheit conversion formula:

\[ F = \frac{9}{5}C + 32 \]

### Step-by-Step Solution:

1. **Rewrite the Conversion Formula**:
We start by rearranging the formula to express Celsius (C) in terms of Fahrenheit (F):
\[ F - 32 = \frac{9}{5}C \]

2. **Multiply Both Sides by 5**:
To eliminate the fraction, multiply both sides by 5:
\[ 5(F - 32) = 9C \]

3. **Distribute the 5**:
Distributing the 5 gives:
\[ 5F - 160 = 9C \]

4. **Solve for C**:
Rearranging this equation gives us:
\[ C = \frac{5F - 160}{9} \]

5. **Set Up the Inequality**:
Since we know the temperature in Fahrenheit is between 50°F and 68°F, we can set up the inequality:
\[ 50 < F < 68 \]

6. **Multiply the Inequality by 5**:
Multiplying the entire inequality by 5 results in:
\[ 250 < 5F < 340 \]

7. **Subtract 160 from All Parts**:
Now, we subtract 160 from each part of the inequality:
\[ 250 - 160 < 5F - 160 < 340 - 160 \]
This simplifies to:
\[ 90 < 5F - 160 < 180 \]

8. **Divide the Inequality by 9**:
Finally, divide the entire inequality by 9 to solve for C:
\[ \frac{90}{9} < \frac{5F - 160}{9} < \frac{180}{9} \]
This simplifies to:
\[ 10 < C < 20 \]

### Conclusion:
The range of temperature in degrees Celsius is:
\[ C \in (10, 20) \]