Sections 1.1 – 1.6: Measurement and Dimensional Anaylsis

How many inches are in [latex]3\frac{1}{2}[/latex] feet?

Solution: Begin by reasoning about your answer. Since a foot is longer than an inch, this means the answer would be greater than [latex]3\frac{1}{2}[/latex] feet. Now state your givens and your goal.

Given: [latex]3\frac{1}{2}[/latex] feet

Goal: Convert to inches, or equivalently, solve [latex]3\frac{1}{2}[/latex] feet = ________inches

1) Find the conversion factor that compares inches and feet, with “inches” in the
numerator, and multiply.

[latex]3\frac{1}{2}[/latex] feet x [latex]\frac{12~inches}{1 foot}[/latex] = ________inches

2) Rewrite the mixed number as an improper fraction before multiplying.

[latex]\frac{7}{2}[/latex] feet x [latex]\frac{12 inches}{1 foot}[/latex] = ________inches  (Since [latex]3\frac{1}{2}[/latex] = [latex]\frac{7}{2}[/latex])

3) You can cancel similar units when they appear in the numerator and the denominator. So here, cancel the similar units “feet” and “foot.” This eliminates this unit from the problem.

[latex]\frac{7~feet}{2}[/latex] x [latex]\frac{12~inches}{1~foot}[/latex] = [latex]\frac{7~\bcancel{feet}}{2}[/latex]  x [latex]\frac{12~inches}{1~\bcancel{foot}}[/latex] = [latex]\frac{7}{2}[/latex] x [latex]\frac{12~inches}{1}[/latex]

4) Rewrite as multiplication of numerators and denominators. Then divide.

[latex]\frac{7}{2}[/latex]  x [latex]\frac{12~inches}{1}[/latex] = [latex]\frac{7~x~12~inches}{2~x~1}[/latex]  = [latex]\frac{84}{2}[/latex] inches = 42 inches

Answer: [latex]3\frac{1}{2}[/latex] feet equals 42 inches.

An interior decorator needs border trim for a home she is wallpapering. She needs 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room. How many yards of border trim does she need?

Solution: State your givens and your goal.

Given: 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room

Goal: How many yards of border trim does she need?

1) You need to find the total length of border trim that is needed for all three rooms in the house. Since the measurements for each room are given in feet, you can add the numbers.

15 feet + 30 feet + 26 feet = 71 feet

2) Observe that our goal is the number of yards, not the number of feet. So we need to convert. How many yards is 71 feet? (Reason about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. Expect your answer to be less than 71.)

71 feet = _____ yards

3) Use the conversion factor [latex]\frac{1~yard}{3~feet}[/latex]

[latex]\frac{71~feet}{1}[/latex] x [latex]\frac{1~yard}{3~feet}[/latex] = _____ yard

4) Since “feet” is in the numerator and denominator, you can cancel this unit. Then rewrite as multiplication of numerators and denominators.

[latex]\frac{71~feet}{1}[/latex] x [latex]\frac{1~yard}{3~feet}[/latex] = [latex]\frac{71~\bcancel{feet}}{1}[/latex] x [latex]\frac{1~yard}{3~\bcancel{feet}}[/latex] = [latex]\frac{71~x~1~yard}{1~x~3}[/latex]

5) Multiply and then rewrite the improper fraction as a mixed number.

[latex]\frac{71~x~1~yard}{1~x~3}[/latex] = [latex]\frac{71}{3}[/latex] yards = [latex]23\frac{2}{3}[/latex]

Answer: The interior designer needs [latex]23\frac{2}{3}[/latex] yards of border trim.

A landscaper is installing artificial turf for a football field. The dimensions of the football field are 120 yards long by 50 yards wide. His supplier sells artificial turf by the square foot. How many square feet of turf is needed for the field?

Solution: State your givens and your goal.

Given: The dimensions of the football field are 120 yards long by 50 yards wide.

Goal: How many square feet of turf is needed for the field?

1) You need to find the total area of the field that needs to be covered. Since both length and width are given in yards, you can multiply. (Note: The resulting units are in square yards.)

120 yards × 50 yards = 6,000 square yards

2) We are asked to find the number of square feet needed. So convert square yards to  square feet. (Reason about the size of your answer. Since a square foot is smaller than a square yard, there will be more square feet. Expect your answer to be larger than 6000.)

[latex]\frac{6,000~yd^2}{1}[/latex] x [latex]\frac{3~ft}{1~yd}[/latex] x [latex]\frac{3~ft}{1~yd}[/latex] = [latex]\frac{6,000~\bcancel{yd}~\bcancel{yd}}{1}[/latex] x [latex]\frac{3~ft}{1~\bcancel{yd}}[/latex] x [latex]\frac{3~ft}{1~\bcancel{yd}}[/latex] = [latex]\frac{6,000~x~3~ft~x~3~ft}{1~x~1~x~1}[/latex] = 54,000 ft²

Answer: The landscaper needs 54,000 square feet of artificial turf for the football field.

A Use the Factor Label Method to determine the number of ounces in [latex]2\frac{1}{4}[/latex] pounds.

Solution: State your givens and your goal.

Given: [latex]2\frac{1}{4}[/latex] pounds

Goal: Determine the equivalent number of ounces

1) Begin by reasoning about your answer. Since a pound is heavier than an ounce, expect your answer to be a number greater than [latex]2\frac{1}{4}[/latex].

[latex]2\frac{1}{4}[/latex] pounds = _______ ounces

2) Multiply by the conversion factor that relates ounces and pounds: [latex]\frac{16~ounces}{1~pound}[/latex]

[latex]2\frac{1}{4}[/latex] pounds x [latex]\frac{16~ounces}{1~pound}[/latex] = _____ ounces

3) Write the mixed number as an improper fraction. The common unit “pound” can be cancelled because it appears in both the numerator and denominator.

[latex]\frac{9~\bcancel{pounds}}{4}[/latex] x [latex]\frac{16~ounces}{1~\bcancel{pound}}[/latex] = _____ ounces

4) Multiply and simplify.

[latex]\frac{9}{4}[/latex] x [latex]\frac{16~ounces}{1}[/latex] = [latex]\frac{9~x~16~ounces}{4~x~1}[/latex] = [latex]\frac{144~ounces}{4}[/latex] = 36 ounces

Answer: There are 36 ounces in [latex]2\frac{1}{4}[/latex] pounds.

A municipal trash facility allows a person to throw away a maximum of 30 pounds of trash per week. Last week, 140 people threw away the maximum allowable trash. How many tons of trash did this equal?

Solution: State your givens and your goal.

Given: maximum of 30 pounds of trash per week per person, 140 people threw away the maximum allowable trash.

Goal: How many tons of trash did this equal?

1) Determine the total trash for the week expressed in pounds. If 140 people each throw away 30 pounds, you can find the total by multiplying.

140 × 30 pounds = 4,200 pounds

2) Then convert 4,200 pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 4,200.

4,200 pounds = _____ tons

3) Find the conversion factor appropriate for the situation: [latex]\frac{1~ton}{2000~pounds}[/latex]

[latex]\frac{4200~\bcancel{pounds}}{1}[/latex] x [latex]\frac{1~ton}{2000~\bcancel{pounds}}[/latex] = _____ tons

4) Multiply and simplify. Rewrite your result as a mixed number.

[latex]\frac{4200}{1}[/latex] x [latex]\frac{1~ton}{2000}[/latex] = [latex]\frac{4200~x~1~ton}{1~x~2000}[/latex] = [latex]\frac{4200}{2000}[/latex] tons = [latex]2\frac{1}{10}[/latex] tons

Answer: The total amount of trash generated is [latex]2\frac{1}{10}[/latex] tons.

The post office charges $0.44 to mail something that weighs an ounce or less. The charge for each additional ounce, or fraction of an ounce, of weight is $0.17. At this rate, how much will it cost to mail a package that weighs 2 pounds 3 ounces?

Solution: State your givens and your goal.

Given: $0.44 to mail something that weighs an ounce or less, each additional ounce of weight is $0.17

Goal: How much will it cost to mail a package that weighs 2 pounds 3 ounces?

1) Since the pricing is for ounces, convert the weight of the package from pounds and ounces into just ounces.

2 pounds 3 ounces = _____ ounces

2) First use the factor label method to convert 2 pounds to ounces.

[latex]\frac{2~\bcancel{pounds}}{1}[/latex] x [latex]\frac{16~oz}{1~\bcancel{pound}}[/latex] = [latex]\frac{2~x~16}{1}[/latex] oz = 32 oz

3) Add the additional 3 ounces to find the weight of the package.

2 pounds 3 ounces = 32 ounces + 3 ounces = 35 ounces

4) Apply the pricing formula. $0.44 for the first ounce and $0.17 for each additional ounce.

$0.44(1) + $0.17(34) = $0.44 + $5.78 = $6.22

Answer: It will cost $6.22 to mail a package that weighs 2 pounds 3 ounces.

Use the Factor Label Method to determine the number of pints in [latex]2\frac{3}{4}[/latex] gallons.

Solution: State your givens and your goal.

Given: [latex]2\frac{3}{4}[/latex] gallons.

Goal: Find the equivalent amount in pints.

1) Begin by reasoning about your answer. Since a gallon is larger than a pint, expect the answer in pints to be a number greater than [latex]2\frac{3}{4}[/latex].

[latex]2\frac{3}{4}[/latex] gallons = _____ pints

2) The table above does not contain a conversion factor for gallons and pints, so you cannot convert it in one step. However, you can use quarts as an intermediate unit, as shown here. Set up the equation so that two sets of labels cancel gallons and quarts.

[latex]2\frac{3}{4}[/latex] gallons = [latex]\frac{11~\bcancel{gallons}}{4}[/latex] x [latex]\frac{4~\bcancel{quarts}}{1~\bcancel{gallon}}[/latex] x [latex]\frac{2~pints}{1~\bcancel{quart}}[/latex] = [latex]\frac{11~X~4~X~2}{4~X~1~X~1}[/latex] pints = 22 pints

Answer: [latex]2\frac{3}{4}[/latex] gallons is equivalent to 22 pints.

Another way to work the problem above would be to first change 1 gallon to 16 cups and change 2 quarts to 8 cups. Then add: 16 + 8 = 24 cups.

Natasha is making lemonade to bring to the beach. She has two containers. One holds one gallon and the other holds 2 quarts. If she fills both containers, how many cups of lemonade will she have?

Solution: State your givens and your goal.

Given: Two containers for lemonade; one holds one gallon and the other holds 2 quarts, fills both containers.

Goal: How many cups of lemonade will she have?

1) This problem requires you to find the sum of the capacity of each container and then convert that sum to cups.

1 gallon + 2 quarts = ___ cups

2) First, find the sum in quarts. 1 gallon is equal to 4 quarts.

4 quarts + 2 quarts = 6 quarts

3) Since the problem asks for the capacity in cups, convert 6 quarts to cups.

[latex]\frac{6~\bcancel{quarts}}{1}[/latex] x [latex]\frac{2~\bcancel{pints}}{1~\bcancel{quart}}[/latex] x [latex]\frac{2~cups}{1~\bcancel{pints}}[/latex] = [latex]\frac{6~X~2~X~2~cups}{1~X~1~X1}[/latex] = 24 cups

Answer: Natasha will have 24 cups of lemonade.

Convert 7,225 centimeters to meters.

Solution: State your givens and your goal.

Given: 7,225 centimeters.

Goal: Find the equivalent length in meters.

1) Meters is larger than centimeters, so you expect your answer to be less than 7,225.

7,225 cm = _____ m

2) Using the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to meters.

[latex]\frac{7,225~cm}{1}[/latex] x [latex]\frac{1~m}{100~cm}[/latex] =  _____ m

3) Cancel similar units, multiply, and simplify.

[latex]\frac{7,225~\bcancel{cm}}{1}[/latex] x [latex]\frac{1~m}{100~\bcancel{cm}}[/latex] = [latex]\frac{7,225~X~1~m}{1~X~100}[/latex] = 72.25 m

Answer: 7,225 centimeters = 72.25 m

In the Summer Olympic Games, athletes compete in races of the following lengths:100 meters, 200 meters, 400 meters, 800 meters, 1500 meters, 5000 meters and 10,000 meters. If a runner were to run in all these races, how many kilometers would he run?

Solution: State your givens and your goal.

Given: The lengths: 100 meters, 200 meters, 400 meters, 800 meters, 1500 meters, 5000 meters and 10,000 meters.

Goal: If a runner were to run in all these races, how many kilometers would he run?

1) To figure out how many kilometers he would run, you need to first add all of the lengths of the races together and then convert that measurement to kilometers.

100 m + 200 m + 400 m + 800 m + 1500 m + 5000 m + 10,000 m = 18,000 m

2) Use the factor label method and unit fractions to convert from meters to kilometers.

[latex]\frac{18,000~m}{1}[/latex] x [latex]\frac{1~km}{1000~m}[/latex] =  _____ km

3) Cancel common units, multiply, and divide.

[latex]\frac{18,000~\bcancel{m}}{1}[/latex] x [latex]\frac{1~km}{1000~\bcancel{m}}[/latex] = [latex]\frac{18,000~X~1~km}{1~X~1000}[/latex] = 18 km

Answer: The runner would run 18 km.

One bottle holds 295 dL while another one holds 28,000 mL. What is the difference in capacity between the two bottles?

Solution: State your givens and your goal.

Given: Two bottle capacities: 295 dL and 28,000 mL.

Goal: What is the difference in capacity between the two bottles?

1) The two measurements are in different units. You can convert both units to liters and then compare them.

2) The question asks for “difference in capacity” between the bottles so we will subtract.

29.5 L – 28 L = 1.5 L

Answer: There is a difference in capacity of 1.5 liters between the two bottles.

A two-liter bottle contains 87 centiliters of oil and 4.1 deciliters of water. How much more liquid is needed to fill the bottle?

Solution: State your givens and your goal.

Given: a 2-Liter bottle contains 87 cL of oil and 4.1 dL of water.

Goal: How much more liquid is needed to fill the bottle?

1) You are looking for the amount of liquid needed to fill the bottle. First determine the amount of liquid already in the bottle by convert both measurements to liters and adding.

Total liquid in bottle: 0.87 L + 0.41 L = 1.28 L

2) Find the difference between 2 L and the amount of liquid in the bottle to see how much more liquid is needed to fill the bottle.

2 L – 1.28 L = 0.72 L

Answer: The amount of liquid needed to fill the bottle is 0.72 liters.

An Olympic sprinter competes in the 400m dash. How many yards is the race?

Solution: State your givens and your goal.

Given: 400m dash

Goal: How many yards is the race?

1) Reason about your answer. A yard is less than a meter, so you expect your answer to be more than 400.

400 m = _____ yd

2) Using the factor label method, write 400 m as a fraction and use unit fractions to convert it to yards.

[latex]\frac{400~m}{1}[/latex] x [latex]\frac{0.9144~yd}{1~m}[/latex] = _____ yd

3) Cancel similar units, multiply, and simplify.

[latex]\frac{400~\bcancel{m}}{1}[/latex] x [latex]\frac{0.9144~yd}{1~\bcancel{m}}[/latex] = [latex]\frac{400~X~0.9144~yd}{1~X~1}[/latex] = 437.45 yd

Answer: A 400 m dash is 437.45 yards.

A patient must be weighed prior to surgery so that the proper dosage of anesthesia can be given. A nurse weighs a patient and finds that he weighs 205 pounds. The anesthesiologist prefers weights in kilograms. What is the patient’s weight in kilograms? Round
to the nearest hundredth.

Solution: State your givens and your goal.

Given: patient weighs 205 pounds

Goal: What is the patient’s weight in kilograms?

1) Reason about your answer. Pounds are smaller than kilograms, so you expect your answer to be less than 205.

205 pounds = _____ kg

2) Using the factor label method, write 205 lbs. as a fraction and use unit fractions to convert it to kilograms.

[latex]\frac{205~lbs}{1}[/latex] x [latex]\frac{1~kg}{2.2~lbs}[/latex] = _____ kg

3) Cancel similar units, multiply, and simplify.

[latex]\frac{205~\bcancel{lbs}}{1}[/latex] x [latex]\frac{1~kg}{2.2~\bcancel{lbs}}[/latex] = [latex]\frac{205~X~1~kg}{2.2}[/latex] = [latex]\frac{205~kg}{2.2}[/latex] ≈ 93.18 kg

Answer: The patient’s weight is 93.18 kg.

Your work is having its annual potluck, and you are asked to bring 5 gallons of lemonade. When you go to the store, each container of lemonade mix says it will make 6 liters. How many containers do you need to buy?

Solution: State your givens and your goal.

Given: Need 5 gallons of lemonade. Lemonade mix says it will make 6 liters.

Goal: How many containers do you need to buy?

1) Convert 5 gallons to liters. Reason about your answer. Liters are smaller than gallons, so you expect your answer to be more than 5.

5 gallons = _____ L

2) Using the factor label method, write 5 gal as a fraction and use unit fractions to convert it to liters. Cancel similar units, multiply, and simplify.

[latex]\frac{5~\bcancel{gallons}}{1}[/latex] x [latex]\frac{3.785~L}{1~\bcancel{gallon}}[/latex] = [latex]\frac{5~X~3.785~L}{1~X~1}[/latex] = 18.925 L

3) You need 18.925 liters, and each container of mix will make 6 liters. Convert to containers.

[latex]\frac{18.925~\bcancel{L}}{1}[/latex] x [latex]\frac{1~container}{6~\bcancel{L}}[/latex] = [latex]\frac{18.925~X~1~container}{6}[/latex] = 3.15 containers

4) Since you cannot buy a partial container, and you want to have enough lemonade, you should buy 4 containers, (3 containers would not be enough)

Answer: You need to buy 4 containers of lemonade.

Your front yard is full of weeds, so you decide to spray it with weed killer. The bottle of weed killer that you purchase says “Do not apply in temperatures below 18°C or above 32°C.” What are the corresponding temperatures in degrees Fahrenheit?

Solution: State your givens and your goal.

Given: Do not apply in temperatures below 18°C or above 32°C

Goal: What are the corresponding temperatures in degrees Fahrenheit?

1) Both temperatures are in degrees Celsius and need to be converted into degrees Fahrenheit. Use F = 1.8C + 32

For C = 18, F = 1.8(18) + 32 = 64.4°F (low temperature)

For C = 32, F = 1.8(32) + 32 = 89.6°F (high temperature)

Answer: The weed killer should only be applied when the temperature is between 64.4°F and 89.6°F.

When leaving the hospital with your sick child, you are told to return immediately if her temperature exceeds 101.5°F. When you get home, you discover your thermometer will only measure temperature in degrees Celsius. At what temperature, in degrees Celsius, would
you need to return your child to the hospital?

Solution: State your givens and your goal.

Given: Return immediately if her temperature exceeds 101.5°F

Goal: At what temperature, in degrees Celsius, would you need to return your child to the hospital?

1) The temperature is in degrees Fahrenheit and it needs to be converted into degrees Celsius. Use C = [latex]\frac{F-32}{1.8}[/latex]

For F = 101.5°F, C = [latex]\frac{101.5 - 32}{1.8}[/latex] = [latex]\frac{69.5}{18}[/latex] = 38.61°C

Answer: You need to return your child to the hospital if her temperature exceeds 38.61°C.

Your car can drive 300 miles on a tank of 15 gallons. Express this as a rate and as a unit rate, in miles per gallon.

Solution: State your givens and your goal.

Given: Your car can drive 300 miles on a tank of 15 gallons.

Goal: Express this as a rate and as a unit rate, in miles per gallon.

1) As a rate, create a fraction with the two quantities with miles in the numerator and gallons in the denominator. Include units in your answer.

[latex]\frac{300~miles}{15~gallons}[/latex]

2) As a unit rate, divide the quantity in the numerator by the quantity in the denominator. Use the “units miles per gallon” (equivalent to miles per 1 gallon).

[latex]\frac{300~miles}{15~gallons}[/latex] = [latex]\frac{300}{15}[/latex] x [latex]\frac{miles}{gallons}[/latex] = 20 miles per gallons

Notice that, had we wanted to find the unit rate in gallons per mile, we would have had to invert the original rate:

[latex]\frac{15~gallons}{300~miles}[/latex] = [latex]\frac{15}{300}[/latex] x [latex]\frac{gallons}{miles}[/latex] = [latex]\frac{1}{20}[/latex] gallons per mile

Use the following information to compare the electricity consumption per capita in China to the rate in Japan.

From the CIA1 website we can find the electricity consumption in 2011 for China was 4,693,000,000,000 KWH (kilowatt-hours), or 4.693 trillion KWH, while the consumption for Japan was 859,700,000,000, or 859.7 billion KWH. To find the rate per capita (per person), we will also need the population of the two countries. From the World Bank2, we can find the population of China is 1,344,130,000, and the population of Japan is 127,817,277.

Solution: State your givens and your goal.

Given: China: 4.693 trillion KWH and 1,344,130,000 people. Japan: 859.7 billion KWH
and 127,817,277 people.

Goal: Computing the consumption per capita for each country and compare the results.

1) Find KWH per person for China and Japan by dividing the quantity KWH by the number of people.

China: [latex]\frac{4,693,000,000,000~KWH}{1,344,130,000~people}[/latex] = 3,491.49 KWH per person

Japan: [latex]\frac{859,700,000,000~KWH}{127,817,277~people}[/latex] = 6,726 KWH per person

Answer: While China uses more than 5 times the electricity of Japan overall, because the population of Japan is so much smaller, it turns out Japan uses almost twice the electricity per person compared to China.

Your car can drive 300 miles on a tank of 15 gallons. How far can it drive on 40 gallons? How many gallons are needed to drive 50 miles?

Solution: State your givens and your goal.

Given: Your car can drive 300 miles on a tank of 15 gallons.

Goals: a) How far can it drive on 40 gallons? b) How many gallons are needed to drive 50 miles?

a) We found that 300 miles on 15 gallons gives a rate of 20 miles per gallon. If we multiply the given 40 gallon quantity by this rate, the gallons unit “cancels” and we’re left with a number of miles.

[latex]\frac{40~\bcancel{gallons}}{1}[/latex] x [latex]\frac{20~miles}{1~\bcancel{gallon}}[/latex] = [latex]\frac{40~x~20}{1~x~1}[/latex] = 800 miles

b) We also found that 300 miles on 15 gallons gives a rate of [latex]\frac{1}{20}[/latex] gallons per mile. If we multiply the given 50 mile quantity by this rate, the miles unit “cancels” and we’re left with gallons.

[latex]\frac{50~\bcancel{miles}}{1}[/latex] x [latex]\frac{1~gallon}{20~\bcancel{miles}}[/latex] = [latex]\frac{50~x~1}{1~x~20}[/latex] gallons = 2.5 gallons

Answers: The car can drive 800 miles on 40 gallons of gas. The car needs 2.5 gallons of gas to drive 50 miles.

A bicycle is traveling at 15 miles per hour. How many feet will it cover in 20 seconds?

Solution: State your givens and your goal.

Given: 15 miles per hour.

Goal: How many feet will the bicycle cover in 20 seconds?

1) To answer this question, we need to convert 20 seconds into feet. If we know the speed of the bicycle in feet per second, this question would be simpler. Since we don’t, we will need to do additional unit conversions. We will need to know that 5280 feet = 1 mile. We might start by converting the 20 seconds into hours:

[latex]\frac{20~\bcancel{sec}}{1}[/latex] x [latex]\frac{1~\bcancel{min}}{60~\bcancel{sec}}[/latex] x [latex]\frac{1~hr}{60~\bcancel{min}}[/latex] hr = [latex]\frac{20}{3600}[/latex] hr = [latex]\frac{1}{180}[/latex] hr

2) Now we can multiply by the 15 miles/hr

[latex]\frac{1~\bcancel{hr}}{180}[/latex] x [latex]\frac{15~mi}{1~\bcancel{hr}}[/latex] = [latex]\frac{15}{180}[/latex] miles = [latex]\frac{1}{12}[/latex] miles

3) Now we can convert to feet.

[latex]\frac{1~\bcancel{mile}}{12}[/latex] x [latex]\frac{5280}{1~\bcancel{mile}}[/latex] = [latex]\frac{5280}{12}[/latex] ft = 440 ft

4) Note we could have also done this entire calculation in one long set of products:

[latex]\frac{20~\bcancel{sec}}{1}[/latex] x [latex]\frac{1~\bcancel{min}}{60~\bcancel{sec}}[/latex] x [latex]\frac{1~\bcancel{hr}}{60~\bcancel{min}}[/latex] x [latex]\frac{15~\bcancel{miles}}{1~\bcancel{hr}}[/latex] x [latex]\frac{5280~ft}{1~\bcancel{mile}}[/latex] = [latex]\frac{20~x~15~x~5280}{60~x~60}[/latex] ft = 440 ft

Answer: The bicycle covers 440 feet in 20 seconds.

You are walking through a hardware store and notice two sales on tubing.

• 3 yards of Tubing A costs $5.49.
• Tubing B sells for $1.88 for 2 feet.

Either tubing is acceptable for your project. Which tubing is less expensive?

Solution: State your givens and your goal.

Given: 3 yards of Tubing A costs $5.49. Tubing B sells for $1.88 for 2 feet.

Goal: Which tubing is less expensive?

1) Find the unit price per yard for each tubing. This will make it easier to compare.

Tubing A: 3 yards for $5.49

Unit price per yard: [latex]\frac{$5.49}{3~yds}[/latex] = [latex]\frac{5.49}{3}[/latex] [latex]\frac{dollars}{yards}[/latex] = $1.83 per yard

Tubing B: 2 feet for $1.88

2) Compare prices for 1 yard of each tubing.

Tubing A: $1.83 per yard

Tubing B: $2.82 per yard

Answer: Tubing A is less expensive than Tubing B.

The cost of gasoline in Arizona is about $2.05 per gallon. When you travel over the border into Mexico, gasoline costs 14.81 pesos per liter. Where is gasoline more expensive? (Note: This problem requires a currency conversion factor. Currency conversions are constantly
changing, but at the time of print $1 = 18.68 pesos.)

Solution: State your givens and your goal.

Given: Gasoline in Arizona is about $2.05 per gallon. Gasoline in Mexico costs 14.81 pesos per liter. $1 = 18.68 pesos

Goal: Where is gasoline more expensive?

1) We will convert the Arizona price from dollars to pesos and gallons to liters to obtain pesos per liter.

[latex]\frac{$2.05}{1~gallon}[/latex] x [latex]\frac{18.68~pesos}{$1}[/latex] x [latex]\frac{1~gallon}{3.8~L}[/latex] = [latex]\frac{2.05~x~18.68}{3.8~L}[/latex] [latex]\frac{pesos}{L}[/latex] = 10.08 pesos per liter

2) Compare the pesos per liter values.

Arizona: 10.08 pesos per liter
Mexico: 14.81 pesos per liter

Answer: Gasoline is more expensive in Mexico.