Ratio form 2 mathematics

7/30/2019 Ratio form 2 mathematics

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CHAPTER 5: RATIOS, RATES, & PROPORTIONS

CHAPTER 5 CONTENTS

5.1 Ratios5.2 Rates5.3 Unit Rates

5.4 Proportions5.5 Applications

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5.1 Ratios (same uni ts)

A ratio is the comparison of two quantities. The quantities may simply be numbers, or the

quantities may be numbers with units attached to them. A ratio may be written in several ways.Suppose that there are 45 cars and 7 trucks in a parking lot. The ratio of trucks to cars can be

written in three ways:

words colon fraction

7 to 45 7 : 45 745

Each is read (expressed verbally) in the same way: 7 to 45. The order in which we write the

parts of a ratio is important. In words and with a colon , we read from left to right. In fraction

form, we read from top to bottom.

Because a ratio can be written as a fraction, it makes sense to reduce a ratio to its lowest

terms in the same way that you would reduce a fraction. Suppose that the width of a building is

540 feet and the height of the building is 80 feet. The ratio the buildings width to its height is

540 to 80. In fraction form, this ratio be expressed 54080

which reduces to 274

.

So, the ratio 540 to 80 can be reduced alsoto the ratio 27 to 4 .

Since ratios are a comparison of two quantities, they are always expressed in fractional form

(proper or improper) but never as a mixed number or a whole number.


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Example 1 : Write the ratio of 5 pounds of apples to 4 pounds of apples in three different ways.

words: 5 to 4 colon: 5:4 fraction:4

5

Example 2 : Write the ratio of $15 to $18 in simplest form.

18

15=

65

318315

Example 3 : Write the ratio of 50 milliliters to 45 milliliters in simplest form.

4550

910

545550

Example 4 : Write the ratio of 8 balls to 11 balls in simplest form.

11

8

Example 5 : Write the ratio of 12 pens to 10 pens in simplest form.

56

210212

1012

Example 6 : Write the ratio of the rectangles length to its width in simplest form.

L = 25 inches

W = 15 inches

25 25 5 515 15 5 3


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5.1 Ratios (same units) Exercises

1. Write the following ratio as a fraction and in words. 5 : 12

2. Write the following ratio using a colon and in words.

3. Write the following ratio as a fraction and using a colon. 18 to 23

In Exercises 4 14, simplify the ratio.

4. 3 : 5

5. 24 : 18

6.

7.

9.

10.

11.

12.

13.

14.

15. The base of a triangle is 60 millimeters, and the height of the triangle is 40 millimeters.What is the ratio of the height to the base?

16. A wheelchair ramp rises 2 feet for every 12 feet it runs. What is the ratio of rise to run?

17. A tree is 12 feet wide and 18 feet high. What is the ratio the trees height to the treeswidth?


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5.1 Ratios (same units) Exercises Answers

1.

2.

3.

4. 3 : 5 is simplified

5. 4 : 3

6.

7.

9.

10.

11.

12.

13.

14.

15.

16.

17.


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5.2 Rates (dif ferent uni ts)

The ratio 11 to 15 may or may not convey the same information as the ratio 15 to 11. Consider a

math class with 11 male students and 15 female students.The ratio of male students to female students is written 11 to 15.

The ratio of female students to male students is written 15 to 11.

Both of these ratios convey the same information about the distribution by gender of students in

a particular math class, even though the ratios are written differently. As fractions (as purely

mathematical entities), however,11

15is not equal to

15

11. Thus, you must always be careful to

distinguish between information and mathematical value.

When the names in a ratio are of different types, the ratio may be called a rate . For instance,

the ratio 150 miles to 3 hours is called a rate. This rate can be written using the word per. It is

also common to write a rate in fraction form; both the word per and a fraction denote the

arithmetic operation of division.

150 miles per 3 hours = 150 miles/3 hours =150 miles

3 hours

Rates are simplified to lowest terms in the same way that ratios are simplified. For instance, if a car can be driven 219 miles using 6 gallons of gasoline, we can talk about the ratio of miles to

gallons or the rate of 219 miles per 6 gallons. This rate may be simplified to lowest terms:

219 miles per 6 gallons =219 miles 73 miles6 gallons 2 gallons

= 73 miles per 2 gallons.

Example 1 : Write the following rate in the simplest form: $50 per 8 pounds

Write the original rate in fraction form. $508 pounds

Simplify the fraction.28250

=$25

4 pounds

Write the meaning of the simplified rate. $25 per 4 pounds


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Example 2: Write the rate in the simplest form: 8 grams of fat per 2 cookies

Write the original rate in fraction form. 82 gramscookies


=41

gramscookie

Write the meaning of the simplified rate. 4 grams of fat per cookie

Example 3 : Write the rate in the simplest form: 126 words in 3 minutes

Write the original rate in fraction form. 1263minutes

words


3126=

421 minute

words

Write the meaning of the simplified rate. 42 words per minute

Example 4 : Write the rate in the simplest form: 8 pounds of apples cost $10

Write the original rate in fraction form. 8$10

pounds


=4

$5 pounds

Write the meaning of the simplified rate. 4 pounds per 5 dollars

Example 5 : Write the rate in the simplest form: 3 tablespoons of olive oil has 42 grams of fat

Write the original rate in fraction form. 342tablespoons

grams


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33= 1

14tablespoon

grams

Write the meaning of the simplified rate. 1 tablespoon of olive oil per 14 grams of fat

5.2 Rates (different units) Exercises Write each rate in simplest fraction form.

1. 36 miles per 6 gallon 2. 10 milliliters per 20 pounds3. 28 grams per 14 milliliters4. 84 pounds per 12 square inches5. $4.00 per 10 boxes6. 12 phone calls in 60 minutes7. 100 pages in 4 hours

8 meters per 10 seconds

9. 48 calories per 3 servings10. 1360 meters in 16 seconds

11. An office assistant can type 1240 words in 20 minutes. Determine therate of words per minute.

12. A runner can complete 28 laps around the track in 14 minutes. What isthe rate of laps per minute for this runner?

13. A patient requires 15 milligrams of medicine for every 35 pounds of weight. What is the rate of milligrams per pound?

14. A box of cereal contains 9 servings. The calories from the entire boxare 750. What is the rate of calories per serving for this cereal?

15. A car traveled 600 miles in 9 hours. What is the rate of miles per hour?

16. On a trip a car traveled 356 miles and used 14 gallons of gas. What isthe rate of miles per gallon?

17. A printer used 5 printer cartridges to print 3480 pages. What is the rate

of printer cartridges to printed pages?18. A grocer scans 32 items in 48 seconds. What is the rate of itemsscanned per second?


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5.2 Rates (different units) Exercises Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.


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18.

5.3 Un it Rates

A unit rate is a rate where the second quantity or the denominator is 1. The following are

examples of unit rates:

5 men to 1 car = 5 men per car = 5 men / car.

30 miles to 1 gallon = 30 miles per gallon = 30 mpg

$3.49 to 1 pound = $3.49 per pound

Any rate can be written as a unit rate by dividing both terms by the second term. For

instance, the rate 200 miles to 8 gallons can be written:

200 miles 8 25 miles200 miles to 8 gallons 25 mpg

8 gallons 8 1 gallon

Sometimes you need to convert one of the units to another type of unit. For instance, you

might be asked to express the rate 15 miles to 20 minutes in miles per hour . You will need to

use the fact that there are 60 minutes in one hour.

15 miles 3 15 miles 45 miles 45 miles45 mph

20 minutes 3 20 minutes 60 minutes 1 hour

One very useful unit rate is called a unit price . Suppose that a 20-ounce box of cereal costs

$3.40. The rate of dollars to ounces is$3.40 $3.40 20

20 ounces 20 20 ounces

$0.171 ounce

= $0.17 per

ounce. That is, 17 per ounce is the unit price.


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Example 1 : The price of 5 pounds of apples is $10. What is the unit rate (price of apples per one

pound)?

Step 1 : Write the original rate $10 to 5 pounds.5

10

Step 2 : Make the denominator equal to 1 by dividing thedenominator by 5 (and, thus, the numerator by 5 also).

10 5 25 5 1

Step 3 : Write the meaning of the simplified unit rate. $2 per pound of apples

Example 2 : Find the unit rate for 240 words in 20 lines.

Step 1 : Write the original rate 240 words to 20 lines.20

240


240 20 1220 20 1

Step 3 : Write the meaning of the simplified unit rate. 12 words per line

Example 3 : Find the unit rate for driving 135 miles on 4 gallons of gasoline

Step 1 : Write the original rate 135 miles to 4 gallons.4

135


135 4 33.754 4 1

Step 3 : Write the meaning of the simplified unit rate. 33.75 miles per gallon


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Example 4 : Mina bought 2.5 kilograms of brown rice for $7.50. Find the unit rate or unit price (of brown rice per kilogram)

Step 1 : Write the original rate $7.5 to 2.5 kg.

5.2

5.7

Step 2 : Make the denominator equal to 1 by dividing thedenominator by 2.5 (and, thus, the numerator by 2.5 also).

7.5 2.5 32.5 2.5 1

Step 3 : Write the meaning of the simplified unit price. $3 per kilogram

Example 5 : A typist can type 2400 words in 40 minutes. Find the unit rate.

Step 1 : Write the original rate 2400 words to 40 minutes. 240040

Step 2 : Make the denominator equal to 1 by dividing thedenominator by 2.5 (and, thus, the numerator by 2.5 also).

2400 40 6040 40 1

Step 3 : Write the meaning of the simplified unit price. 60 words per minute


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5.3 Unit Rate Exercises Determine the unit rate.

1. 784 calories per 4 servings of pie2. 550 miles in 11 hours

3. 345 miles per 12 gallons4. $15.20 per 3 hours5. 34 grams per 17 milliliters6. 120 pages in 6 hours7. 28 meters per 8 seconds

$8.25 per 3 boxes9. $45.35 per 5 hours10. 8700 calories per 15 servings

11. A phone call from New York City to Nairobi, Kenya costs $9.35 for 32 minutes. What isthe price per minute this telephone call?

12. At the SuperOgre grocery store, there is a sale on Scampb ulls soup: 10 cans of Turkey-n-Comets soup cost $8.22. What is the price per can of soup?

13. After her morning coffee, an administrative assistant can type 2435 words in 20 minutes.What is the administrative assistants unit rate in words per minute?

14. A 12- ounce can of Bushs Original Baked B eans costs $.88. What is the unit price per

ounce?

15. Elmer owns a delivery service, FuddEx. One of the vehicles in his fleet traveled 120 milesin 2 hours. What is the unit rate in miles per hour that the delivery vehicle traveled?

16. Anne babysat her twin nieces for 6 hours and was paid $36. What is her pay per hour?

17. Four peanut butter cookies have 125 calories. How many calories are there per cookie?

18. Lakisha bought 5 Granny Smith apples for $1.50. What is the unit price per apple?

19. William got a bill for his texting overages: $2.25 for 25 texts. How much was he charged per text?

20. Lance Legstrong rode his bicycle 10 miles in 30 minutes. What is the unit rate in miles per hour that he bicycled?


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5.3 Unit Rates Exercises Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15. or 60 miles per hr .

16.

17.

18.

19.

20.


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5.4 Proportions

A proportion is a statement that two ratios are equal. For instance,1 23 6

and3 24 7

are

proportions. A proportion is either true or false. Because13 and

2

6 are equivalent fractions, the

first proportion is true. Because3

4and

2

7are not equivalent fractions, the second proportion is

false.

The proportiona cb d

is read a is to b as c is to d . This proportion can be written in colon

form as a : b :: c : d , where a and d are called the extremes , and b and c are called themeans.

A proportion is true if and only if the product of the extremes equals the product of the

means. Therefore,a cb d

is true if and only if a d b c . ad and bc are called the cross

products. Thus, a proportion is true if and only if its cross products are equal. For instance, the

proportion4 6

22 33is true because 433 = 226; both cross products equal 132 and are, thus

equal to each other. The proportion1.2 0.97 5

is false because (1.2)(5) = 6 is not equal to

(7)(0.9) = 6.3.

A proportion has four numbers. If only three of the numbers are given, and a variablerepresents the fourth, you can solve for the missing number by assuming that the proportion istrue. To solve a proportion for the missing number n :

1. Cross multiply and set the two cross products equal to each other. This creates an equation inthe variable n.

2. Solve this equation for n by dividing both sides of the equation by the number that ismultiplied with n.

For instance, to solve the proportion17 10051 n

for the value of n, cross multiply, obtaining

17n = 51100. Then, divide both sides of the equation by 17, yielding n = 300.


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Example 1 : Is1815

65

a true statement?

If the product of 5 and 18 is equal to the product of 6 and 15, then the proportion is true.

6 15 5 18

90 = 90 Therefore, the proportion is true.

Example 2 : Solve for n:n

1032

Calculate the cross products, and equate them. 2 3 10n

302n

To solve for n, divide by 2. 230n 15n

Example 3 : Solve for n:5.25.1

5.7n

Calculate the cross products, and equate them. 2.5 7.5 1.5n

25.115.2 n

To solve for n, divide by 2.5. 5.225.11n 5.4n

Example 4 : Solve for n:

123 95 5

n

Calculate the cross products, and equate them. 3 1 95 2 5

n

109

53 n

To solve for n, divide by35 . 5

3109

n35

109 45

3045 1530 15

23

n


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Example 5 : Solve for n:453

n

Calculate the cross products, and equate them. 5 3 4n

125n

To solve for n, divide by 5. 512n

512

n

= 2.4

Example 6 : Solve for n:

12

41 1

12 2

n

Convert each mixed fraction to an improper fraction.

2 4 11 92

4 9 4and

1 2 11 31

2 2 2

The proportion has become 9

41 32 2

n

Calculate the cross products, and equate them. 3 1 92 2 4

n

89

23

n

To solve for n, divide by 32 . 9 38 2n 9 2

8 31824

18 624 6

34

n


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5.4 Proportion Exercises

1. Is the following proportion true or false?




5. Solve the following proportion for n.

6. Solve the following proportion for r .

7. Solve the following proportion for b.


9. Solve the following proportion for u.

10. Solve the following proportion for v.

11. Solve the following proportion for a .

12. Solve the following proportion for s.


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14. Solve the following proportion for t .

15. Solve the following proportion for r .

3

21

2

4r

16. Solve the following proportion for b.5

6

124

b

17. Solve the following proportion for a .9

8

2

3 5a

18. Solve the following proportion for p.3

8

5

91

12

p

19. Solve the following proportion for t .4

7

1

21

12

3 t

20. Solve the following proportion for s.1

32

22

36 s


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5.4 Proportions Exercises Answers 1. False proportion2. True proportion3. True proportion4. False proportion

5. 15 = n

6. r = 2

7. b = 16

8. n = 69

9. u =

10. v =

11. a = 4.9

12. 5 = s

13. n = 2.2729 (rounded)

14. t = 5.12

15.

16.

17.

18.

19. t = 24


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20.


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5.5 Applications

There are several types of applications which can be solved using ratios and proportions.

The first type of application is to split an amount according to a given ratio. For instance, the

lawyer and the plaintiff of a successful lawsuit are going to divide the $22,000 judgment

according to the ratio 4:6. The lawyer receives 4 parts (each part is of an equal amount), and the

plaintiff receives 6 parts. The $22,000 is split into 4 + 6 = 10 equal parts, and each part is worth

$22,000/10 = $2,200. The portion allotted to the lawyer is 4 x $2,200= $8,800, and the plaintiff

receives 6 x $2,200= $13,200.

In working with mixtures or recipes, the ratio of ingredient A to ingredient B to ingredient C

might be 2:3:5. If there is a total of 20 ounces of the mixture, how much of each ingredient

should be used?

To apportion an amount according to a given ratio:

1. Add the terms of the ratio together.

2. Divide the total amount to be apportioned by this sum. This gives one part.

3. Multiply the value of one part by each term in the ratio. The answers represent the

apportioned amounts.

To apportion 20 ounces according to the ratio 2:3:5, we first add 2 + 3 + 5 = 10 parts.

Then, 20 ounces/10 parts simplifies to 2 ounces per part. Thus, there are 2x 2 = 4 ounces of

ingredient A, 2x3 = 6 ounces of ingredient B, and 2x 5 = 10 ounces of ingredient C .

Another type of application is to compare two ratios or rates such as unit prices. Which is a

better buy: a 6-ounce can of tuna for $1.20 or a 10-ounce can of tuna for $1.60? To decide,

compare the unit prices. The unit price of the 6-ounce can is $1.20/6 = $.20, and the unit price

for the 10-ounce can is $1.60/10 = $.16. The 10-ounce can of tuna is the better buy because it

has a lesser unit price.


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Proportions can be used to solve applications whose quantities are proportional. Two

quantities are proportional if doubling one means the other will double, tripling one means the

other will triple, halving one means the other will halve, and so on.

Suppose you know that there are 56 milligrams of cholesterol in1

32

ounces of trout. How

much cholesterol is contained in 8 ounces of trout?

To solve using proportions :

1. Let x (or another variable) represent the unknown quantity.

2. Use the information in the problem to write two ratios.

3. Write the first ratio based on known information in fraction form, including

the units.

4.

Write the second ratio so that the units of its numerator match the units of thefirst ratios numerator, and so that the units of its denominator match the units

of the first ratios denominator .

5. Make a proportion by setting the ratios equal, and solve the proportion.


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The question How much cholesterol is contained in 8 ounces of trout? indicates that the

unknown quantity is the number of milligrams of cholesterol in 8 ounces of trout.

Let x = the number of milligrams of cholesterol in 8 ounces of trout.

The first ratio is56 milligrams

13 ounces2

and the second ratio ismilligrams8 ounces

x.

Thus, we must solve the proportion561 83 2

x.

Convert the mixed fraction to an improper fraction.

3 2 11 73

2 2 2

The proportion has become 567 82

x

Calculate the cross products, and equate them. 756 8

2 x

7448

2 x

To solve for x, divide by7

2 .7

4482

x448 21 7

8967

896 7

128 x mg of cholesterol

Always remember to include the appropriate units in your answer.


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Example 1: A single tablet of One-A-Day Vitamin for men contains 60 milligrams of VitaminC. How many milligrams of vitamin C are in 4 tablets of One-A-Day Vitamin?

Step 1 : Assign a variable to the unknown quantity. Let n = the number of mg. of Vitamin C in 4 tablets.

Step 2 : Write the first ratio based on known information:one tablet contains 60 milligrams of Vitamin C.

160tablet

mg

Step 3 : Write the second ratio with the unknown quantity.Make sure that the units of the respective numerators matchand the units of the respective denominators match.

4 tabletsn mg

Step 4 : Write a proportion.n4

601

Step 5 : Solve the proportion for the variable by equatingcross products.

6041 n

2401n

240 240 1 2401

n

There are 240 milligrams of vitamin C in 4 tablets of One-A-Day Vitamin.


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Example 2: To make pink lemonade, Bruce mixes 36 grams of pink lemonade powder with 5quarts of water. How much pink lemonade powder would be needed to mix with 15 quarts of water?

Step 1 : Assign a variable to the unknown quantity. Let n = the number of grams of powder for 15 quarts of water.

Step 2 : Write the first ratio based on known information:36 grams of powder are needed for 5 quarts of water.

365

gramsquarts


15n grams

quarts

Step 4 : Write a proportion.155

36 n


15365 n

5 540n

540540 5 108

5n

Bruce needs 108 grams of pink lemonade powder to mix with 15 quarts of water.


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Example 3: Water is pumped out of a basement at a rate of 140 gallons per hour. How manyhours will it take to pump 2030 gallons of water out of the basement?

Step 1 : Assign a variable to the unknown quantity. Let n = the number of hours to pump out 2030 gallons of water.

Step 2 : Write the first ratio based on known information:140 gallons of water are pumped out in 1 hour.

1401

gallonshour


2030 gallonsn hours

Step 4 : Write a proportion.n

20301

140


140 2030 1n

2030140n

20302030 140 14.5

140n

It will take 14.5 hours to pumps out 2030 gallons of water.


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Example 4: There are 36 grams of fat in an 8-ounce steak. How many grams of fat are there in a12-ounce steak?

Step 1 : Assign a variable to the unknown quantity. Let n = the number of grams of fat in a 12-ounce steak.

Step 2 : Write the first ratio based on known information:there are 36 grams of fat in an 8-ounce steak.

368

grams of fat ounces of steak


12n grams of fat ounces of steak


36 n


12368 n

4328n

432 432 8 548

n

There are 54 grams of fat in a 12-ounce steak.


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Example 5: You need to combine 98 grams of sulfuric acid (H 2SO4) and 80 grams of sodiumhydroxide (NaOH) to produce sodium sulfate (a kind of chemical salt). How many grams of sulfuric acid (H 2SO4) would you need to combine with 20 grams of sodium hydroxide (NaOH)to produce sodium sulfate?

Step 1 : Assign a variable to the unknown quantity. Let n = the number of grams of H2SO4 to combine with 20grams of NaOH.

Step 2 : Write the first ratio based on known information:98 grams of H 2SO4 are needed for 80 grams of NaOH

2 49880

grams of H SO grams of NaOH


2 4

20n grams of H SO

grams of NaOH


98 n


209880 n

196080n

19601960 80 24.5

80n

24.5 grams of sulfuric acid (H 2SO4) are needed to combine with 20 grams of sodium hydroxide(NaOH) to produce sodium sulfate.


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5.5 Application Exercises Solve the following proportions.

1. Harrys truck gets 23 miles per gallon of gasoline. If his truck has 4 gallons of gasoline, howfar can the truck go?

2. Barry wants to make a 720-ounce solution with 3 parts water, 4 parts alcohol, and 5 partsglucose. How many ounces of each substance would he use to make the solution?

3. On a map, 3 inches represents 8 miles. How many inches will represent a distance of 48miles?

4. On a map, 2 cm represents 3 kilometers. How many kilometers are represented by 15 cm?

5. A nurse has to give a patient a dose of medication. The dosage says 3 ml of medication for a150-pound person. If the person weighs 200 pounds, how many milliliters of medication is the

person to receive?6. Four milligrams of a drug are to be given for every 10 kilograms of body weight. Find theweight of a person requiring 25 milligrams of the drug.

7. To make one pound of lemonade mix you need 120 grams of sugar. How much sugar do youneed for 2 pounds of mix? How much sugar do you need for 0.5 pounds of mix?

8. A nurse has to give a child a dose of Tylenol. The dosage says 2 teaspoons of medication for a 50-pound child. If the child weighs 75 pounds, how many teaspoons of medication should thechild receive?

9. A recipe calls for teaspoon of salt for every cup of flour. How much salt should beused for 5 cups of flour?

10. A baker can make 72 cookies using 4 cups of flour. How many cups of flour are needed tomake 288 cookies?

11. Three ounces of a chemical are needed to treat 25 ounces of water. How many ounces of the chemical are needed to treat 100 ounces of water?

12. To make 4 moles of water, 2 moles of oxygen gas are needed. How many moles of water can you make with 21 moles of oxygen gas?

13. A child care center advertises that it has a ratio of 2 caregivers for every 9 children. If thereare 6 caregivers, how many children are at the child care center?


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14. A college has a ratio of 2 male students for every 3 female students. If there are 5322 malestudents at the college, how many female students attend the college?

15. An office assistant can type 525 words in 5 minutes. At this rate, how many words can the

office assistant type in 20 minutes?

16. A baseball player gets 36 hits in 90 times at bat. At this rate, how many hits should he getin 250 times at bat?

17. There are 45 mg of cholesterol in 2 ounces of egg substitute. How many mg of cholesterolare there in 3 ounces of egg substitute?

18. There are 18 grams of fat in a 4-ounce steak. How many grams of fat are there in a 6-ouncesteak?

19. At the grocery store, a 16-ounce bag of rice costs $2.34, and a 24-ounce bag of rice costs$3.42. Which is the better buy?

20. At a warehouse store, you can purchase 60 cans of soda for $8.95. At a regular grocery store,you can purchase 12 cans of soda for $1.85. Which is the better deal?


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5.5 Proportion Application Exercises Answers 1. 92 miles ; Harry will be able to go 92 miles on 4 gallons of gas2. 180 ounces of water, 240 ounces of alcohol, and 300 ounces of glucose 3. 18 inches ; 18 inches will represent 24 miles on a map4. 22.5 km ; 22.5 km will represent 3 cm on a map5. 4 ml ; the nurse will give the person 4 milliliters of medication6. 62.5 kg ; 25 mg will be given to a person who weighs 62.5 kg 7. 240 g (for 2 pounds of mix); 60g (for 0.5 pounds of mix)8. 3 tsps ; 3 tsps of Tylenol are given to a person weighing 75 lbs9. 2.5 tsps ; 2.5 tsps of salt will be used for 5 cups of flour 10. 16 cups ; 16 cups of flour are needed to make 288 cookies 11. 12 ounces of chemical ; 12 ounces of chemical are needed for 100 ounces of water 12. 42 moles of water ; 42 moles of water can make 21 moles of gas

13. 27 children ; 27 children are at the childcare 14. 7983 female students ; 7983 female students attend the college 15. 2100 words ; the office assistant can type 2100 words in 20 minutes 16. 100 hits ; the player can get 100 hits in 250 times at bat17. 67.5 mg ; there are 67.5 milligrams of cholesterol in 3 ounces of egg substitute18. 27 grams of fat ; there are 27 grams of fat in a 6-ounce steak 19. The 16-ounce bag is $.146/oz and the 24-ounce bag is $.142/oz; therefore, the24-ounce bag is the better buy.20. The 60 cans are $.149/can, the 12 cans are $.154 /can; therefore, the 60 cans are thebetter deal.

Ratio form 2 mathematics

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