Chapter 8.4, Problem 50STP

To determine

What is the temperature in degrees Fahrenheit. The formula is $C=\frac{5}{9}(F-32)$ .

Answer to Problem 50STP

  $95°\text{F}$

Explanation of Solution

Given:

The formula is $C=\frac{5}{9}(F-32)$ . temperature is $35°\text{C}$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the temperature in degrees Fahrenheit, first subtituting 35 for C in the formula $C=\frac{5}{9}(F-32)$ , then solving it, first multiply both sides by 9/5 and then add 32 both sides and to simplify further as shown below:

  $\begin{array}{l}C=\frac{5}{9}(F-32)\\ 35=\frac{5}{9}(F-32)\\ \frac{9}{5}\cdot 35=\frac{5}{9}\cdot \frac{9}{5}(F-32)\\ 63=F-32\\ 63+32=F-32+32\\ 95=F\end{array}$

So, the temperature in degrees Fahrenheit is $95°\text{F}$