Math Help for Section 3.3, Page 121
Example
5: Tip
Both of these problems fit question type #3 from the guide in the Math Help on page 119:
| Question$\quad\quad\quad\quad$ | Given | Percent Equation | |
| 3. | a is what percent of b? |
a and b | Solve for p. |
Example
5: Check
| a. |
$\eqalign{135 =& p(27)&{\small\color{red}\quad\quad\text{Write original equation.}} \cr 135\overset{?}{=}&\left({\color{red}5} \right)(27)&{\small\color{red}\quad\quad\text{Substitute 5 for }p.} \cr 135 =& 135&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr} $ |
| b. | $\eqalign{8092.5 =& p(124,500)&{\small\color{red}\quad\quad\text{Write original equation.}} \cr 8092.5 \overset{?}{=}&\left({\color{red}0.065} \right)(124,500)&{\small\color{red}\quad\quad\text{Substitute 0.065 for }p.} \cr8092.5 =&8092.5&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr}$ |
Study
Tip
Recall from Section 1.4 that some fractional numbers can be represented
by repeating decimals. To represent these numbers, you can put a bar
over the repeated digit(s). For instance,
$\displaystyle{4\over{1800}} =
0.00222… = 0.00\overline 2 .$
You can use this equivalence when finding percents. Here is an
example.
| Question: | 4 is what percent of 1800? | |
| Solution: | $\quad\quad\;\;4 = p\left( {1800} \right)$ |
Substitute values into percent equation. |
| $\displaystyle{4 \over {1800}} = p\quad\quad$ |
Divide each side by 1800. |
Once you have $p ={4 \over {1800}},$ you can write it as a
repeating decimal, then convert it to a percent:
$\displaystyle{4 \over {1800}} =
0.00\overline 2 = 0.00\overline 2 \left( {100\% } \right) =
0.\overline 2 \% $
or you can leave it a fraction, convert it to a percent, and
then reduce the fraction:
$\displaystyle{4 \over {1800}} = {4
\over {1800}}\left( {100\% } \right) = {{400} \over {1800}}\%
= {{2 \bullet \cancel{200}} \over {9 \bullet
\cancel{200}}}\% = {2 \over 9}\% $
$0.\overline 2 \% $ is equivalent to ${2 \over 9}\% .$