Math Help for Section 3.4, Page 132
Solving Proportions
One way to write a proportion is to use a table.
| Triangular Lot |
Sketch | |
| Shorter Side | 100 ft | 8 in. |
| Longer Side | 210 ft | x in. |
Use the columns or the rows to write a proportion.
| $\displaystyle{{100}{\text{ ft}} \over {210}{\text{ ft}}} = {8{\text{ in.}} \over x{\text{ in.}}}$ |
Equate a ratio of the sides of the lot to a ratio of the sides of the sketch. Each ratio has the same units in its numerator and denominator. This is the proportion used in the textbook on page 132. |
|
| $\displaystyle{{100}{\text{ ft}} \over 8{\text{ in.}}} = {{210}{\text{ ft}} \over x{\text{ in.}}}$ |
Equate a ratio of the shorters sides to a ratio of the longer sides. Numerators have the same units and denominators have the same units. |
These proportions both result in the same solution, $x=16.8$ inches.
Example
6: Check
$\eqalign{ {{100} \over {210}}
=& {8 \over
x}&{\small\color{red}\quad\quad\text{Write original
equation.}} \cr {{100} \over {210}} \overset{?}{=}&
{8 \over {\color{red}16.8}}&{\small\color{red}\quad\quad\text{Substitute 16.8 for }x.} \cr 0.476… =&
0.476…&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr} $