Chapter 2 Approaches to Problem Solving

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Chapter 2Approaches to Problem Solving
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Section 2A

• Units
• Pages 84-95

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

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2-A
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Practice what units?

• The price of apples, found by dividing their
  total cost in dollars by their total weight in
  pounds.
• dollars per pound /lb
• The density of a rock, found by dividing its
  weight in grams by its volume in cubic
  centimeters.
• grams per cubic centimeter g/c3 g/cc
• A car engine torque, calculated by multiplying a
  force in pounds by a distance in feet.
• foot-pounds ft-lbs

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Unit Conversions
2-A

• Trick multiply by 1.

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Unit Conversions
2-A

• Convert a distance of 9 feet into inches.
• How many minutes are in one week?

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Unit Conversions
2-A

• Using the fact that there are 1760 yards in a
  mile and 3 feet in a yard, convert a distance of
  3 miles into feet.

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Unit Conversions
2-A

• A football field is 100 yards long and 60 yards
  wide. Find its area in (a) square yards and (b)
  square feet.
• (a)
• (b)

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Unit Conversions
2-A

• A car is driving 70 mile per hour. What is its
  speed in miles per second?

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Unit Conversions
2-A

• Recall this room had an area of 2530 750ft2.
  
• Convert the area to in2 (square inches).

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Problem Solving with Units
2-A

• Example You are buying 50 acres of farm land at
  a cost of 12,500 per acre. What is the total
  cost?
• The answer should be in dollars. We multiply
  acreage by the cost per acre

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Problem Solving with Units
2-A

• You take a trip in which you drive 1200 miles in
  20 hours. What is your average speed for the
  trip?
• The answer should be in mph. We divide miles
  traveled by time (hours) traveled

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Problem Solving with Units
2-A

• A human heart beats about 60 times per minute.
  If an average human being lives to the age of 80,
  how many times does the average heart beat in a
  lifetime?

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Currency Conversions (Feb. 5, 2007)www.xe.com
2-A

Currency Dollars per foreign Foreign per Dollar
British pound 1.9597 .510281
Canadian dollar 0.846067 1.18194
European euro 1.29262 0.773624
Japanese yen 0.00830818 120.363
Mexican peso 0.0915788 10.9196
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Buying currency
2-A

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

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Buying currency
2-A

• You return from a trip with 2500 Mexican pesos.
  How much are your pesos worth in US ?

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Buying currency
2-A

• Apples in Japan sell for about 75 yen each. If
  you buy 4 apples, how much have you spent in
  dollars?

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Buying currency
2-A

• How many Canadian dollars can you buy for 100?

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Example What went wrong?
2-A

• You ride your bike up a steep mountain road at 5
  mph. How far do you go in 3 hours?
• Student solution
• Should be 5 miles/hour 3 hours 15 miles

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Example What went wrong?
2-A

• A candy store sells chocolate for 7.70 per
  pound. The piece you want to buy weighs 0.11 lb.
  How much will it cost, to the nearest cent?
  (Ignore sales tax.)
• Student solution
• Should be 7.77/lb .11 lb .85

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Homework for Monday

• Pages 97-99
• 32, 35, 50, 53, 65, 68, 75
• Use the exchange rates given to you in class.