A solution is to be kept between `59^(@) F and 77^(@)` F. What is the range of temperature in degree celcius (C) if the Celcius-farhenheit conversion formula is:
` F =(9)/(5) C + 32`

Explanation

To find the range of temperature in degrees Celsius corresponding to the Fahrenheit range of 59°F to 77°F, we will use the conversion formula from Fahrenheit to Celsius:

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

### Step 1: Set up the inequality
We know that the temperature in Fahrenheit (F) is between 59°F and 77°F. Therefore, we can express this as:

\[ 59 < F < 77 \]

### Step 2: Substitute the conversion formula into the inequality
Now, we substitute the Fahrenheit conversion formula into the inequality:

\[ 59 < \frac{9}{5}C + 32 < 77 \]

### Step 3: Isolate the term with C
To isolate the term with C, we first subtract 32 from all parts of the inequality:

\[ 59 - 32 < \frac{9}{5}C < 77 - 32 \]

This simplifies to:

\[ 27 < \frac{9}{5}C < 45 \]

### Step 4: Eliminate the fraction
Next, we multiply the entire inequality by \(\frac{5}{9}\) to eliminate the fraction:

\[ \frac{5}{9} \cdot 27 < C < \frac{5}{9} \cdot 45 \]

Calculating the left side:

\[ \frac{5 \cdot 27}{9} = \frac{135}{9} = 15 \]

Calculating the right side:

\[ \frac{5 \cdot 45}{9} = \frac{225}{9} = 25 \]

### Step 5: Write the final result
So we have:

\[ 15 < C < 25 \]

This means the range of temperature in degrees Celsius is:

\[ C \in (15, 25) \]

### Final Answer
The range of temperature in degrees Celsius is between 15°C and 25°C.

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