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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
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What is meant by 'nano scale'?
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What is STMs full form?
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scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
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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.
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anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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what does nano mean?
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nano basically means 10^(-9). nanometer is a unit to measure length.
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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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