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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 [link] we noted that many practical problems can be solved by writing the given information as proportions. Such proportions will be composed of three specified numbers and one unknown number represented by a letter.

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:
  1. By careful reading, determine what the unknown quantity is and represent it with some letter. There will be only one unknown in a problem.
  2. Identify the three specified numbers.
  3. Determine which comparisons are to be made and set up the proportion.
  4. Solve the proportion (using the methods of [link] ).
  5. 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 → 2 inches 25 miles size 12{ { {"2 inches"} over {"25 miles"} } } {}
    8 inches to x miles → 8 inches x miles size 12{ { {"8 inches"} over {"x miles"} } } {}
    Proportions involving ratios and rates are more readily solved by suspending the units while doing the computations.
    2 25 = 8 x size 12{ { {2} over {"25"} } = { {8} over {x} } } {}
  • 2 25 = 8 x Perform the cross multiplication.
    2 x = 8 25 2 x = 200 Divide 200 by 2. x = 200 2 x = 100
    In step 1, we let x size 12{x} {} represent the number of miles. So, x size 12{x} {} represents 100 miles.
  • If 2 inches represents 25 miles, then 8 inches represents 100 miles.
    Try [link] in [link] .

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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 → 7 2 size 12{ { {7} over {2} } } {}
    n size 12{n} {} parts water to 20 parts acid → n 20 size 12{ { {n} over {"20"} } } {}
    7 2 = n 20 size 12{ { {7} over {2} } = { {n} over {"20"} } } {}
  • 7 2 = n 20 Perform the cross multiplication.
    7 20 = 2 n 140 = 2 n Divide 140 by 2. 140 2 = n 70 = n
    In step 1 we let n size 12{n} {} represent the number of parts of water. So, n size 12{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] .

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A 5-foot girl casts a 3 1 3 size 12{ { {1} over {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 = height of the person size 12{h=" height of the person"} {} .
  • The three specified numbers are
    5 feet ( height of girl)
    3 1 3 size 12{3 { {1} over {3} } } {} feet (length of shadow)
    3 feet (length of shadow)
  • The comparisons are
    5-foot girl is to 3 1 3 size 12{3 { {1} over {3} } } {} foot shadow → 5 3 1 3 size 12{ { {5} over {3 { {1} over {3} } } } } {}
    h -foot person is to 3-foot shadow → h 3 size 12{ { {h} over {3} } } {}
    5 3 1 3 = h 3 size 12{ { {5} over {3 { {1} over {3} } } } = { {h} over {3} } } {}
  • 5 3 1 3 = h 3
    5 3 = 3 1 3 h 15 = 10 3 h Divide 15 by 10 3 15 10 3 = h 15 3 1 3 10 2 = h 9 2 = h h = 4 1 2
  • A person who casts a 3-foot shadow at this particular time of the day is 4 1 2 size 12{4 { {1} over {2} } } {} feet tall.
    Try [link] in [link] .

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Questions & Answers

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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