Math Help for Section 3.3, Page 119
The
Percent Equation
There are three variables in the percent equation, so there are three
basic types of percent problems. You can solve each of them by
substituting the two given quantities into the percent equation and
solving for the third quantity. The three types of problems are as
follows.
| Question$\quad\quad\quad\quad$ | Given | Percent Equation | |
| 1. | What number is p percent of b? |
p and b | Solve for a. |
| 2. | a is p percent of what number? |
a and p | Solve for b. |
| 3. | a is what percent of b? |
a and b | Solve for p. |
Example
3: Check
| a. | $\eqalign{a =& \left({0.3} \right)\left( {70} \right)&{\small\color{red}\quad\quad\text{Write original equation.}} \cr \color{red}21\color{black} \overset{?}{=}& \left( {0.3} \right)\left({70} \right)&{\small\color{red}\quad\quad\text{Substitute 21 for {\it a}.}} \cr 21 =& 21&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr} $ |
| b. | $\eqalign{a =& {0.07}\left( {40,240} \right)&{\small\color{red}\quad\quad\text{Write original equation.}} \cr \color{red}2816.80\color{black} \overset{?}{=}& {0.07}\left( {40,240} \right)&{\small\color{red}\quad\quad\text{Substitute 2816.80 for }a.} \cr 2816.80 =& 2816.80&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr} $ |
Both of these problems fit question type #1 from the guide above.