Math Help for Section 3.5, Page 136

Using
Formulas
In
some applications, it helps to rewrite a common formula by solving for
a different variable. For instance, using the common formula for
temperature, you can obtain a formula for C (degrees Celsius)
in terms of F
(degrees Fahrenheit) as follows.

    $\eqalign{F =& {9 \over 5}C +
32&{\small\color{red}\quad\quad\text{Temperature
formula}}  \cr F – 32 =& {9 \over
5}C&{\small\color{red}\quad\quad\text{Subtract 32 from
each side.}}  \cr {5 \over 9}\left( {F – 32} \right)
=& C&{\small\color{red}\quad\quad\text{Multiply each
side by }{5 \over 9}.}  \cr C =& {5 \over
9}\left(
{F – 32} \right)&{\small\color{red}\quad\quad\text{Formula}}
\cr} $

    One of the most familiar rate
problems and most often used formulas in real life is the one that
relates distance, rate (or speed), and time: $d = rt.$ For instance, if
you travel at a constant (or average) rate of 50 miles per hour for 45
minutes, the total distance traveled is given by

    $d = rt = \left(
{50\;\displaystyle{{\text{miles}} \over{\cancel{\text{hour}}}}}
\right)\left( {\displaystyle{{45} \over {60}}{\cancel{ \text{hour}}}}
\right) =
37.5{\text{ miles.}}$

Notice that the time is converted from 45 minutes to ${45
\over 60}$ hour so that hours will cancel out and the answer
will be given in miles. 

Technology:
Tip

You can use this simple
interest calculator to check your answer for simple interest
problems. Enter the three known values and click CALCULATE to find the
unknown value. Use the calculator to check the results of Example 1.
You must enter 0.5 for time because 6 months is half of a year. Then
use the calculator to find P
when $I = \$ 5269,$ $r = 11\% ,$ and $t = 5$ years.

  
 Show
Answer

Example
1: Check

    $\eqalign{ 162.50 =& 5000\left( r
\right)(0.5)&{\small\color{red}\quad\quad\text{Write original
equation.}}  \cr 162.50 \overset{?}{=}& 5000\left(
{\color{red} 0.065}
\right)(0.5)&{\small\color{red}\quad\quad\text{Substitute 0.065
for }r.} \cr 162.50\overset{?}{=}& 325
\bullet (0.5)&{\small\color{red}\quad\quad\text{Multiply.}} 
\cr 162.50 =&
162.50&{\small\color{red}\quad\quad\text{Solution
checks. }\checkmark}
\cr} $