Chapter 2 Approaches to Problem Solving

1
Chapter 2Approaches to Problem Solving

• Section 2A
• The Problem Solving Power of Units
• Pages 84-95

2
Units

• The units of a quantity describe what is being
  measured or counted.
• We can add or subtract numbers ONLY when they
  have the same units.
• We can always multiple or divide numbers well
  just create new units.

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For example

• Travel 195 miles (distance)
• Trip took 3 hours (time)
• Average speed (distance/time)
• 195 miles/3 hours
• 65 mph (miles per hour)

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For example

• One side of the floor is 25 feet long
• The other side is 30 feet long.
• The area of the floor space
• 25 ft 30 ft 750 ft2 (square feet)
• The rooms height is 12 feet.
• The volume of the room is
• 25ft 30ft 12ft 9000 ft3 9000 cubic feet

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2-A
6
Practice what units?

• 19/96 The price of apples, found by dividing
  their
• total cost in dollars by their total weight in
  pounds.
• dollars per pound /lb
• 1b/85 The area of a circle, found with the
  formula
• where r is the radius of the circle measured in
  centimeters.
• - square centimeters cm2
• 27/97 The density of a rock, found by dividing
  its weight in grams by its volume in cubic
  centimeters.
• grams per cubic centimeters g/c3 g/cc
• pg85 The energy used by a light bulb found by
  multiplying the power rating in kilowatts by the
  number of hours it is turned on.
• - kilowatt X hours kilowatt-hours

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Unit Conversionsconverting one set of units to
another
2-A

• Trick multiply by 1.

12 inches 1 foot
1 week 7 days
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Unit Conversions
2-A

• 30/97 Convert a distance of 18 yards into inches.

33/97 Convert a lot size of 1/5 acre to square
feet.(1 acre 43560 square feet)
38/97 A car is driving at 100 kilometers per
hour. What is its speed in kilometers per second?
44/97 A football field is 100 yards long and
60 yards wide. Find its area in square yards
and square feet. (Careful with square and cubic
units!)
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Currency Conversions (www.xe.com on 8/29/06)
2-A
Currency dollars per foreign foreign per Dollar
British pound 1.89198 0.528548
Canadian dollar 0.899786 1.11138
European euro 1.27605 0.783671
Japanese yen 0.00855457 116.897
Mexican peso 0.0917226 10.9024

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Currency Conversions
2-A

• 49/97 Which is worth more today 1 British pound
  or 1 dollar? Explain.

51/97 You return from a trip with 2500 Mexican
pesos. How much are your pesos worth in ?
54/97 How many Canadian dollars can you buy for
100?
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Problem Solving with Units
2-A
56/97 Apples in Japan sell for about 75 yen each.
If you buy 4 apples, how much have you spent in
dollars?

• 57/98 A car travels 14 miles in 15 minutes. How
  fast is it going in miles per hour?
• 59/98 You purchased 40 acres of farm land for
  200,000. How much did you pay per acre?
• 61/98 You are buying 4.7 pounds of apples priced
  at 1.29 per pound. How much do you pay?
• 66/98 You are buying artificial turf to cover a
  game field that is 150 feet long and 100 feet
  wide. The turf costs 7.50 per square yard. How
  much do you pay?

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2-A
Problem Solving with Units
70/98 A human heart beats about 60 times per
minute. If an average human being lives to the
age of 75, how many times does the average heart
beat in a lifetime?
75/98 Suppose you drive a car with an average
gas mileage of 28 miles per gallon. If you plan
to take a 2500-mile cross country trip, how many
gallons of gasoline should you expect to use.
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Homework

• Pages 97-99
• Part I 34, 45, 48, 53, 54 55, 58, 62, 65,
  68, 76
• use the exchange rates given to you in class.
• Part II 58, 60, 62, 65, 68, 76