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The ratio of men to women in a particular town is 3 to 5. How many women are there in the town if there are 19,200 men in town?

  • The unknown quantity is the number of women in town.
    Let x = number of women in town.
  • The three specified numbers are
    3
    5
    19,200
  • The comparisons are 3 men to 5 women → 3 5 size 12{ { {3} over {5} } } {}
    19,200 men to x size 12{x} {} women → 19 , 200 x size 12{ { {"19","200"} over {x} } } {}
    3 5 = 19 , 200 x size 12{ { {3} over {5} } = { {"19","200"} over {x} } } {}
  • 3 5 = 19,200 x
    3 x = 19,200 5 3 x = 96,000 x = 96,000 3 x = 32,000
  • There are 32,000 women in town.

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The rate of wins to losses of a particular baseball team is 9 2 size 12{ { {9} over {2} } } {} . How many games did this team lose if they won 63 games?

  • The unknown quantity is the number of games lost.
    Let n = number of games lost.
  • Since 9 2 size 12{ { {9} over {2} } } {} → means 9 wins to 2 losses, the three specified numbers are
    9 (wins)
    2 (losses)
    63 (wins)
  • The comparisons are
    9 wins to 2 losses→ 9 2 size 12{ { {9} over {2} } } {}
    63 wins to n size 12{n} {} losses → 63 n size 12{ { {"63"} over {n} } } {}
    9 2 = 63 n size 12{ { {9} over {2} } = { {"63"} over {n} } } {}
  • 9 2 = 63 n
    9 n = 2 63 9 n = 126 n = 126 9 n = 14
  • Step 5: This team had 14 losses.
    Try [link] in [link] .

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Practice set a

Solve each problem.

On a map, 3 inches represents 100 miles. How many miles are represented by 15 inches?





















500 miles

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An alcohol solution is composed of 14 parts water to 3 parts alcohol. How many parts of alcohol are in a solution that is composed of 112 parts water?





















24 parts of alcohol

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A 5 1 2 size 12{5 { {1} over {2} } } {} -foot woman casts a 7-foot shadow at a particular time of the day. How long of a shadow does a 3-foot boy cast at that same time of day?





















3 9 11 size 12{3 { {9} over {"11"} } } {} feet

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The rate of houseplants to outside plants at a nursery is 4 to 9. If there are 384 houseplants in the nursery, how many outside plants are there?





















864 outside plants

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The odds for a particular event occurring are 11 to 2. (For every 11 times the event does occur, it will not occur 2 times.) How many times does the event occur if it does not occur 18 times?





















The event occurs 99 times.

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The rate of passing grades to failing grades in a particular chemistry class is 7 2 size 12{ { {7} over {2} } } {} . If there are 21 passing grades, how many failing grades are there?





















6 failing grades

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Exercises

For the following 20 problems, use the five-step method to solve each problem.

On a map, 4 inches represents 50 miles. How many inches represent 300 miles?

24

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On a blueprint for a house, 2 inches represents 3 feet. How many inches represent 10 feet?

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A model is built to 2 15 size 12{ { {2} over {"15"} } } {} scale. If a particular part of the model measures 6 inches, how long is the actual structure?

45 inches

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An acid solution is composed of 5 parts acid to 9 parts of water. How many parts of acid are there in a solution that contains 108 parts of water?

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An alloy contains 3 parts of nickel to 4 parts of silver. How much nickel is in an alloy that con­tains 44 parts of silver?

33 parts

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The ratio of water to salt in a test tube is 5 to 2. How much salt is in a test tube that contains 35 ml of water?

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The ratio of sulfur to air in a container is 4 45 size 12{ { {4} over {"45"} } } {} . How many ml of air are there in a container that contains 207 ml of sulfur?

2328.75

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A 6-foot man casts a 4-foot shadow at a particu­lar time of the day. How tall is a person that casts a 3-foot shadow at that same time of the day?

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A 5 1 2 size 12{5 { {1} over {2} } } {} -foot woman casts a 1 1 2 size 12{1 { {1} over {2} } } {} -foot shadow at a particular time of the day. How long a shadow does her 3 1 2 size 12{3 { {1} over {2} } } {} -foot niece cast at the same time of the day?

21 22 size 12{ { {"21"} over {"22"} } } {} feet

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A man, who is 6 feet tall, casts a 7-foot shadow at a particular time of the day. How tall is a tree that casts an 84-foot shadow at that same time of the day?

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The ratio of books to shelves in a bookstore is 350 to 3. How many books are there in a store that has 105 shelves?

12,250

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The ratio of algebra classes to geometry classes at a particular community college is 13 to 2. How many geometry classes does this college offer if it offers 13 algebra classes?

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The odds for a particular event to occur are 16 to 3. If this event occurs 64 times, how many times would you predict it does not occur?

12

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The odds against a particular event occurring are 8 to 3. If this event does occur 64 times, how many times would you predict it does not occur?

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The owner of a stationery store knows that a 1-inch stack of paper contains 300 sheets. The owner wishes to stack the paper in units of 550 sheets. How many inches tall should each stack be?

1 5 6 size 12{1 { {5} over {6} } } {}

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A recipe that requires 6 cups of sugar for 15 serv­ings is to be used to make 45 servings. How much sugar will be needed?

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A pond loses 7 1 2 size 12{7 { {1} over {2} } } {} gallons of water every 2 days due to evaporation. How many gallons of water are lost, due to evaporation, in 1 2 size 12{ { {1} over {2} } } {} day?

1 7 8 size 12{1 { {7} over {8} } } {}

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A photograph that measures 3 inches wide and 4 1 2 size 12{4 { {1} over {2} } } {} inches high is to be enlarged so that it is 5 inches wide. How high will it be?

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If 25 pounds of fertilizer covers 400 square feet of grass, how many pounds will it take to cover 500 square feet of grass?

31 1 4 size 12{"31" { {1} over {4} } } {}

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Every 1 1 2 size 12{1 { {1} over {2} } } {} teaspoons of a particular multiple vitamin, in granular form, contains 0.65 the mini­mum daily requirement of vitamin C. How many teaspoons of this vitamin are required to supply 1.25 the minimum daily requirement?

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Exercises for review

( [link] ) Find the product, 818 0 size 12{"818" cdot 0} {} .

0

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( [link] ) Determine the missing numerator: 8 15 = N 90 size 12{ { {8} over {"15"} } = { {N} over {"90"} } } {} .

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( [link] ) Find the value of 3 10 + 4 12 19 20 size 12{ { { { {3} over {4} } + { {4} over {"12"} } } over { { {"19"} over {"20"} } } } } {} .

2 3 size 12{ { {2} over {3} } } {}

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( [link] ) Subtract 0.249 from the sum of 0.344 and 0.612.

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( [link] ) Solve the proportion: 6 x = 36 30 size 12{ { {6} over {x} } = { {"36"} over {"30"} } } {} .

5

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
7hours 36 min - 4hours 50 min
Tanis Reply

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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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