Math Help for Section 3.3, Page 124
Additional
Example
A
playground has an area of 17,000 square feet. A rectangular basketball
court with a length of 92 feet and a width of 45 feet is built in the
playground. What percentage of the playground is occupied by the
basketball court?
Solution
Solve the problem by
writing a verbal
model using the percent equation, assigning labels, writing, and solving an algebraic equation.
| Verbal Model: |
$\boxed{\eqalign{&\text{Area of} \cr &\text{court}}}\;=\; \boxed{\eqalign{&\text{Percent (in} \cr &\text{decimal form)}}}\;\bullet\;\boxed{\eqalign{&\text{Area of} \cr &\text{playground}}} $ |
||
| Labels: | Area of court $=(92)(45)$ | (square feet) | |
| Percent $=p$ | (decimal form) | ||
| Area of playground $=17,000$ | (square feet) | ||
| Equation: | $\eqalign{(92)(45)=&p(17,000)}$ | ||
You can solve this equation as follows.
$\eqalign{(92)(45)=&p(17,000)
&{\small\color{red}\quad\quad\text{Write equation.}}
\cr 4140=&p(17,000)
&{\small\color{red}\quad\quad\text{Multiply.}}
\cr {4140\over{17,000}}=&p
&{\small\color{red}\quad\quad\text{Divide each side by 17,000.}} \cr 0.244\approx&p
&{\small\color{red}\quad\quad\text{Simplify.}}} $
So, the area of the basketball court is about 24.4% of the area of the playground.