This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses applications of proportions. By the end of the module students should be able to solve proportion problems using the five-step method.
Section overview
The Five-Step Method
Problem Solving
The five-step method
In
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The first and most important part of solving a proportion problem is to determine, by careful reading, what the unknown quantity is and to represent it with some letter.
The five-step method
The five-step method for solving proportion problems:
By careful reading, determine what the unknown quantity is and represent it with some letter. There will be only one unknown in a problem.
Identify the three specified numbers.
Determine which comparisons are to be made and set up the proportion.
Solve the proportion (using the methods of
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Interpret and write a conclusion in a sentence with the appropriate units of measure.
Step 1 is extremely important. Many problems go unsolved because time is not taken to establish what quantity is to be found.
When solving an applied problem,
always begin by determining the unknown quantity and representing it with a letter.
Problem solving
Sample set a
On a map, 2 inches represents 25 miles. How many miles are represented by 8 inches?
The unknown quantity is miles.
Let
$x=$ number of miles represented by 8 inches
The three specified numbers are
2 inches
25 miles
8 inches
The comparisons are
2 inches to 25 miles →
$\frac{\text{2 inches}}{\text{25 miles}}$ 8 inches to x miles →
$\frac{\text{8 inches}}{\text{x miles}}$ Proportions involving ratios and rates are more readily solved by suspending the units while doing the computations.
$\frac{2}{\text{25}}=\frac{8}{x}$
$\begin{array}{cccc}\hfill \frac{2}{25}& =& \frac{8}{x}\hfill & \text{Perform the cross multiplication.}\hfill \end{array}$ $\begin{array}{cccc}\hfill 2\cdot x& =& 8\cdot \mathrm{25}\hfill & \\ \hfill 2\cdot x& =& 200\hfill & \text{Divide 200 by 2.}\hfill \\ \hfill x& =& \frac{200}{2}\hfill & \\ \hfill x& =& 100\hfill & \end{array}$ In step 1, we let
$x$ represent the number of miles. So,
$x$ represents 100 miles.
If 2 inches represents 25 miles, then 8 inches represents 100 miles.
Try
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An acid solution is composed of 7 parts water to 2 parts acid. How many parts of water are there in a solution composed of 20 parts acid?
The unknown quantity is the number of parts of water.
Let
$n=$ number of parts of water.
The three specified numbers are
7 parts water
2 parts acid
20 parts acid
The comparisons are
7 parts water to 2 parts acid →
$\frac{7}{2}$ $n$ parts water to 20 parts acid →
$\frac{n}{\text{20}}$ $\frac{7}{2}=\frac{n}{\text{20}}$
$\begin{array}{cccc}\hfill \frac{7}{2}& =& \frac{n}{\mathrm{20}}\hfill & \text{Perform the cross multiplication.}\hfill \end{array}$ $\begin{array}{cccc}\hfill 7\cdot \mathrm{20}& =& 2\cdot n\hfill & \\ \hfill 140& =& 2\cdot n\hfill & \text{Divide 140 by 2.}\hfill \\ \hfill \frac{140}{2}& =& n\hfill & \\ \hfill 70& =& n\hfill & \end{array}$ In step 1 we let
$n$ represent the number of parts of water. So,
$n$ represents 70 parts of water.
7 parts water to 2 parts acid indicates 70 parts water to 20 parts acid.
Try
[link] in
[link] .
A 5-foot girl casts a
$3\frac{1}{3}$ -foot shadow at a particular time of the day. How tall is a person who casts a 3-foot shadow at the same time of the day?
The unknown quantity is the height of the person.
Let
$h=\text{height of the person}$ .
The three specified numbers are
5 feet ( height of girl)
$3\frac{1}{3}$ feet (length of shadow)
3 feet (length of shadow)
The comparisons are
5-foot girl is to
$3\frac{1}{3}$ foot shadow →
$\frac{5}{3\frac{1}{3}}$ h -foot person is to 3-foot shadow →
$\frac{h}{3}$ $\frac{5}{3\frac{1}{3}}=\frac{h}{3}$
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry