# 7.3 Applications of proportions  (Page 2/2)

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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 → $\frac{3}{5}$
19,200 men to $x$ women → $\frac{\text{19},\text{200}}{x}$
$\frac{3}{5}=\frac{\text{19},\text{200}}{x}$
• $\begin{array}{cccc}\hfill \frac{3}{5}& =& \frac{19,200}{x}\hfill & \end{array}$
$\begin{array}{cccc}\hfill 3\cdot x& =& 19,200\cdot 5\hfill & \\ \hfill 3\cdot x& =& 96,000\hfill & \\ \hfill x& =& \frac{96,000}{3}\hfill & \\ \hfill x& =& 32,000\hfill & \end{array}$
• There are 32,000 women in town.

The rate of wins to losses of a particular baseball team is $\frac{9}{2}$ . 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 $\frac{9}{2}$ → 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→ $\frac{9}{2}$
63 wins to $n$ losses → $\frac{\text{63}}{n}$
$\frac{9}{2}=\frac{\text{63}}{n}$
• $\begin{array}{cccc}\hfill \frac{9}{2}& =& \frac{63}{n}\hfill & \end{array}$
$\begin{array}{cccc}\hfill 9\cdot n& =& 2\cdot \mathrm{63}\hfill & \\ \hfill 9\cdot n& =& 126\hfill & \\ \hfill n& =& \frac{126}{9}\hfill & \\ \hfill n& =& 14\hfill & \end{array}$
• Step 5: This team had 14 losses.

## Practice set a

Solve each problem.

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

500 miles

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

A $5\frac{1}{2}$ -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?

$3\frac{9}{\text{11}}$ feet

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

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.

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

## 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

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

A model is built to $\frac{2}{\text{15}}$ scale. If a particular part of the model measures 6 inches, how long is the actual structure?

45 inches

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?

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

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?

The ratio of sulfur to air in a container is $\frac{4}{\text{45}}$ . How many ml of air are there in a container that contains 207 ml of sulfur?

2328.75

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?

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

$\frac{\text{21}}{\text{22}}$ feet

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?

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

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?

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

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?

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?

$1\frac{5}{6}$

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?

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

$1\frac{7}{8}$

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

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

$\text{31}\frac{1}{4}$

Every $1\frac{1}{2}$ 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?

## Exercises for review

( [link] ) Find the product, $\text{818}\cdot 0$ .

0

( [link] ) Determine the missing numerator: $\frac{8}{\text{15}}=\frac{N}{\text{90}}$ .

( [link] ) Find the value of $\frac{\frac{3}{10}+\frac{4}{\text{12}}}{\frac{\text{19}}{\text{20}}}$ .

$\frac{2}{3}$

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

( [link] ) Solve the proportion: $\frac{6}{x}=\frac{\text{36}}{\text{30}}$ .

5

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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what is the stm
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
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LITNING
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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
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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 .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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what is Nano technology ?
write examples of Nano molecule?
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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?
what king of growth are you checking .?
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why we need to study biomolecules, molecular biology in nanotechnology?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
7hours 36 min - 4hours 50 min