Deck 2: Approaches to Problem Solving

Question 1

Solve the problem.
Paul and Saul ran a 50-meter race. When Paul crossed the finish line, Saul had run only 48
meters. Then they ran a second race, with Paul starting 2 meters behind the starting line.
Assuming that both runners ran at the same pace as in the first race, who won the second
race?

Answer 1

Paul

Question 2

Decide whether the statement makes sense. Explain your reasoning.
I donated 64 fluid ounces of blood today.

Answer 2

Does not make sense. The units are fine, but 64 fluid ounces are equivalent to 4
pints. A typical blood donation is one pint; donating four pints would be
dangerous. (Explanations will vary.)

Question 3

Solve the problem.
Suppose that China's population policy is modified so that every family could have
children until either a boy is born or two children are born, whichever comes first.
Assuming that every family chooses to have as many children as possible under this
policy, and that boys and girls are equally likely, how many children would be born in a
typical group of 1000 families?

Answer 3

1500

Question 4

Decide whether the statement makes sense. Explain your reasoning.
I got pulled over by a police officer for speeding. I was going 150 kiloliters per second.

Question 5

Solve the problem.
It takes you 84 seconds to walk from the first (ground)floor of a building to the fourth
floor. How long will it take to walk from the first floor to the 8th floor (at the same pace,
assuming that all floors have the same height)?

Question 6

Solve the problem.
Abe, Boris, Cal, and David all proposed to Ellie on Friday. Abe proposed at 5:00, Boris
proposed at 6:00, Cal proposed at 7:00, and David proposed at 8:00. Ellie accepted the last
of the four proposals. Some clues: (1)The times may be A.M. or P.M. (2)Boris proposed
before Abe (3)At least one suitor proposed between the proposals of Cal and David. (4)
Cal did not propose between Boris and Al. Whose proposal did Ellie accept?

Question 7

Decide whether the statement makes sense. Explain your reasoning.
To convert square yards to square inches, I multiplied by

Question 8

Decide whether the statement makes sense. Explain your reasoning.
To convert from Kelvin to Celsius, you subtract 273.15. For example, -100 K = -373.15 °C.

Question 9

Solve the problem.
Cheddar cheese comes in 2-pound bags, and mozzarella cheese comes in 5-pound bags.
Using entire bags, you make a 47-pound mixture of cheese. How many bags of each type
of cheese did you use? Find all the possible solutions to the problem.

Question 10

Decide whether the statement makes sense. Explain your reasoning.
I can walk on my hands for 5 meters before falling down, but my goal is to walk a full
decimeter without losing my balance.

Question 11

Decide whether the statement makes sense. Explain your reasoning.
My friend wants to lose 15 pounds, but I think that's too much. I think 10 kilograms would
make more sense.

Question 12

Decide whether the statement makes sense. Explain your reasoning.
The container was big enough to hold a barrel of water, but it wasn't big enough to hold a
barrel of petroleum.

Question 13

Decide whether the statement makes sense. Explain your reasoning.
We will need 1800 cubic feet of carpeting to cover the floors in our three-story house.

Question 14

Solve the problem.
You are considering buying 15 silver coins that look alike, but you have been told that one
of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a
maximum of three weighings on a balance scale?

Question 15

Solve the problem.
Suppose that 8 turns of a wire are wrapped around a pipe with a length of 60 inches and a
circumference of 4 inches. What is the length of the wire?

Question 16

Solve the problem.
Three boxes are labeled "CDs," "DVDs," and "CDs & DVDs." Each label is wrong. Bey
selecting just one item from just one box, how can you determine the correct labeling of the
boxes?

Question 17

Solve the problem.
Two bicyclists, 42 miles apart, begin riding toward each other on a long straight avenue.
One cyclist travels 15 miles per hour and the other 20 miles per hour. At the same time,
Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as
they approach each other. If Spot runs 38 miles per hour and turns around instantly at each
cyclist, how far has he run when the cyclists meet?

Question 18

Decide whether the statement makes sense. Explain your reasoning.
If you complete the four-step problem-solving process carefully and thoroughly, then you
will have no uncertainty about your final answer.

Question 19

Decide whether the statement makes sense. Explain your reasoning.
The boat leaked and started filling with water. There must be 50 gallons of water in it
already.

Question 20

Solve the problem.
There is a large jar of marbles, containing red, blue, yellow, black, and white marbles. How
many marbles must you draw (without looking)from the jar to be sure of getting at least
three of one color?

Question 21

Decide whether the statement makes sense. Explain your reasoning.
Our utility company charges 10 cents per joule for the energy we use.

Question 22

Solve the problem.
How do you measure 6 minutes with a 7-minute hourglass and a 5-minute hourglass?
Assume that the hourglasses can only measure 7-minute and 5-minute intervals,
respectively, and cannot be used to measure other time intervals.

Question 23

State how much larger or smaller the first unit is than the second.
gigagram, microgram

Question 24

Decide whether the statement makes sense. Explain your reasoning.
I figured out the number of seconds in a week by multiplying 7 by 24 by 60 by 60.

Question 25

Solve the problem.
How many square inches are in 6 square yards?

Question 26

Decide whether the statement makes sense. Explain your reasoning.
Whether it's a problem in mathematics or something else, I always find it's best to complete
the work by looking back to check, interpret, and explain my solution.

Question 27

Solve the problem.
Suppose that you have 10 white socks and 6 black socks in a clothes dryer. How many
socks must you withdraw from the dryer (without looking)to be certain of having a pair of
white socks?

Question 28

Solve the problem.
A father and son are in a terrible car accident. The father is killed. The son, badly injured, is
brought to the hospital for emergency surgery. The surgeon takes one look at the patient
and exclaims, "That's my son!" How is this possible?

Question 29

Solve the problem.
A curved bridge rises over a canyon. The two endpoints of the bridge are one mile apart
horizontally. The bridge rises to a height of 353 feet above the horizontal. Approximately
what is the walking distance along the bridge, in feet?

Question 30

Solve the problem.
A traffic counter consists of a thin black tube stretched across a street or highway and
connected to a "brain box" at the side of the road. The device registers one "count" each
time a set of wheels (that is, wheels on a single axle)rolls over the tube. A normal
automobile (two axles)registers two counts, and a light truck (three axles)registers three
counts. Suppose that, during a one-hour period, a particular counter registers 41 counts on
a residential street on which only two-axle vehicles (cars)and three-axle vehicles (light
trucks)are allowed. How many cars and light trucks passed over the traffic counter? Find
all the possible solutions to the problem.

Question 31

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate.

Question 32

Solve the problem.
There are 20 bags filled with coins that all look alike. The coins in 19 of the bags are
authentic and weigh 10 ounces each. The coins in one of the bags are counterfeit and weigh
11 ounces each. With only one weighing on a scale, how can you determine which bag
contains the counterfeit coins?

Question 33

Solve the problem.
Suppose that you begin with a red bucket containing 12 red marbles and a yellow bucket
containing 12 yellow marbles. You move three marbles from the red bucket to the yellow
bucket, and then you move any four marbles from the yellow bucket to the red bucket.
Which is greater, the number of yellow marbles in the red bucket or the number of red
marbles in the yellow bucket?

Question 34

Solve the problem.
A trader bought a stock for $70 and then sold it for $80. He bought it back for $89 and then
sold it again for $99. How much did he gain or lose on these transactions?

Question 35

Decide whether the statement makes sense. Explain your reasoning.
It is not recommended that you use approximations to solve a problem, because then your
solution is only an approximation.

Question 36

Decide whether the statement makes sense. Explain your reasoning.
I drove really far, almost 200 kilometers per hour.

Question 37

Write as a common fraction.

Question 38

Decide whether the statement makes sense. Explain your reasoning.
I found a rock at the bottom of our swimming pool. It had a mass of 500 grams and a
volume of 1000 cubic centimeters, so its density was 0

Question 39

Solve the problem.
A curved bridge rises over a river, so that the two endpoints of the bridge are 160 yards
apart horizontally. You walk across the bridge with a device to measure its length and
discover that the walking distance is 168 yards. Approximately how high does the bridge
rise above the horizontal?

Question 40

Decide whether the statement makes sense. Explain your reasoning.
I figured out the distance we had traveled by dividing our speed by the amount of time we
had traveled.

Question 41

Solve the problem.
There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms.

Question 42

Decide which of the two given prices is the better deal.
You can buy hair product in a 12-ounce bottle for $2.88 or in a 8-ounce bottle for $1.76.

A)8-ounce bottle for $1.76
B)equal value
C)12-ounce bottle for $2.88
D)not enough information

Question 43

Solve the problem.
A warehouse is 42 yards long and 26 yards wide with a height of 13 yards. What is the volume of the warehouse?

Question 44

Convert the measurement to the units specified. Round your answer to the nearest tenth.
15 cubic inches to milliliters

A)0.5 milliliters
B)0.9 milliliters
C)245.7 milliliters
D)443.6 milliliters

Question 45

Evaluate.

Question 46

Evaluate.

Question 47

Decide which of the two given prices is the better deal.
The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 10-oz bottles for $2.30
Seven 12-oz bottles for $4.20

A)Five 10-oz bottles
B)not enough information
C)Seven 12-oz bottles
D)equal value

Question 48

Use units to help you answer the question. If necessary, round your answer to two decimal places.
A stockbroker sold 35 shares of stock for $40.31 each. What was the total amount of the sale?

A)$1410.95
B)$1410.96
C)$1410.85
D)$1410.75

Question 49

Solve the problem.

A)1,000,100,000
B)1,000,010,000
C)10,000,000,000,000
D)100,010,000

Question 50

Solve the problem.

Question 51

Carry out the indicated unit conversion. Round your answer, if appropriate.

A)968 square feet
B)9680 square feet
C)979 square feet
D)9790 square feet

Question 52

State how much larger or smaller the first unit is than the second.
centiliter, microliter

A)Smaller by a factor of 1000
B)Larger by a factor of 1000
C)Smaller by a factor of 10,000
D)Larger by a factor of 10,000

Question 53

Solve the problem.
A 14-gram object has a volume of 35 cubic centimeters. Find its density.

Question 54

Convert the measurement to the units specified. Round your answer to the nearest tenth.
23 feet to meters

A)21 meters
B)7 meters
C)9.1 meters
D)75.4 meters

Question 55

Write as a common fraction.

Question 56

Answer the following question involving a conversion within the USCS system.
How many gallons are in 79 barrels of petroleum?

A)3318 gal
B)1.9 gal
C)4108 gal
D)2449 gal

Question 57

State how much larger or smaller the first unit is than the second.
gram, milligram

Question 58

Solve the problem.
A piece of land in Ottawa with an area of 0.5 square kilometers is priced at 5800 Canadian dollars. If there are 0.9965 Canadian dollars per (U.S.)dollar, then what is the price in dollars per square
Mile?

A)$30,147.74 per square mile
B)$4494.76 per square mile
C)$29,937.07 per square mile
D)$18,733.45 per square mile

Question 59

Solve the problem.
Your electrical bill states that you used 800 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules.

A)256,000,000 joules
B)288,000,000 joules
C)2,560,000,000 joules
D)2,880,000,000 joules

Question 60

Solve the problem.
What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour?

A)30 cents
B)60 cents
C)67 cents
D)45 cents

Question 61

Evaluate.

Question 62

Identify the units you would expect for the given quantity.
The price of pudding, found by dividing its cost in dollars by its weight in ounces.

A)ounce-dollars
B)dollars per ounce
C)dollar-ounces
D)ounces per dollar

Question 63

Convert the measurement to the units specified. Round your answer to the nearest tenth.
93 kilometers per hour to miles per hour

A)128.6 miles per hour
B)149.7 miles per hour
C)57.8 miles per hour
D)67.9 miles per hour

Question 64

Use units to help you answer the question. If necessary, round your answer to two decimal places.
A paint mixture contains 5 gallons of base for every gallon of color. In 108 gallons of paint, how many gallons of color are there?

A)90 gal
B)36 gal
C)18 gal
D)54 gal

Question 65

Carry out the indicated unit conversion. Round your answer, if appropriate.
A car is driving at 180 miles per hour. What is its speed in miles per minute?

A)648,000 miles per minute
B)240 miles per minute
C)3 miles per minute
D)10,800 miles per minute

Question 66

Solve the problem.

Question 67

Solve the problem.
You burn 300 Calories will exercising for 40 minutes. What is your average power while exercising, in watts?

A)784.5 watts
B)523 watts
C)627.6 watts
D)418.4 watts

Question 68

Carry out the indicated unit conversion. Round your answer, if appropriate.
Use a chain of conversions with familiar measures of time to convert 8 weeks into seconds.

A)4,838,400 seconds
B)691,200 seconds
C)201,600 seconds
D)80,640 seconds

Question 69

Carry out the indicated unit conversion. Round your answer, if appropriate.
Convert a weight of 16 pounds into ounces; there are 16 ounces in 1 pound.

A)320 ounces
B)128 ounces
C)256 ounces
D)512 ounces

Question 70

Identify the units you would expect for the given quantity.
The amount of electricity utilized, calculated by multiplying power in kilowatts by time in hours.

A)kilowatt-hours
B)kilowatts per second
C)hours per kilowatt
D)kilowatts per hour

Question 71

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate.

Question 72

Solve the problem.

Question 73

Solve the problem.

Question 74

Answer the following question involving a conversion within the USCS system.
A boat is moving at 48 miles per hour. What is its speed in knots (nautical miles per hour)?

A)57.2 knots
B)39.7 knots
C)55.2 knots
D)41.7 knots

Question 75

Solve the problem.
An object has a total volume of 5 liters (which is 5000 cubic centimeters)and a mass of 4 kilograms. What is its density? Will it sink or float in water?

Question 76

Evaluate.

Question 77

Solve the problem.

Question 78

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate.

Question 79

Solve the problem.
How many cubic furlongs are in a cubic mile? (1 mile = 8 furlongs)

A)64 cubic furlongs
B)4096 cubic furlongs
C)512 cubic furlongs
D)8 cubic furlongs

Question 80

Use the following table of exchange rates to solve the problem. Round your answer when appropriate.
How many Mexican pesos can you buy for $180?

A)14,999.4 pesos
B)2.16 pesos
C)2291.4 pesos
D)14.139 pesos