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Use Your Knowledge of English: 

Insurance statistics state that a person loses 8 minutes of average life for each cigarette smoked. If there are 20 cigarettes in a pack and the average cost of cigarettes are $5.00 per pack over the next 25 years, how many years of average life would a person lose for smoking 1.5 packs a day for 25 years?

_???__years avglife = 25 yearssmoking

1. From the Problem write down all the Equivalent Relationships given or Unit Factors.
  • 8 minutesavglife = 1 cigsmoking
  • 20 cig = 1 pack
  • 1 pack = 5.00 dollars
  • 1.5 pack = 1 daysmoking
2. Beware of our Tricks!

  • We disguise numbers by making them words.

    each cig equates to 1 cig

  • We leave out obvious equivalent relationships, or relationships we think you should know.

    365 days = 1 year
    60 minutes = 1 hour
    24 hour = 1 day
    (I also use to leave out 20 cig = 1 pack in this problem)

  • We stick extra information in the form of numbers and equivalent relationship you will not need to solve the problem

    the average cost of cigarettes are $5.00 per pack






3. Formulate a road map which connects the unit of the given to the unit of the answer by equivalent relationships.

The Question:

____???____ yrlifelost = 25 yrsmoking

Given Unit Factors

  • 1 cig = 8 minlifelost
  • 1 pack = 20 cig
  • 1 pack = 5.00 dollars
  • 1 day = 1.5 packsmoking

Unit Factors Not Given

  • 1 yr = 365 days (or 365.25 days)
  • 1 day = 24 hr
  • 1 hr = 60 min


The Solution:

1. The important bridge between life lost and smoking is the
8 minutes lost = 1 cig smoked Unit Factor.

2. Connect 25 years of smoking to total cigarettes via the unit factor
1.5 packs = 1 day smoking

3. Change years of smoking to days of smoking
then to total packs,
then to total cigarettes.

4. Next change the 8 minutes of life to years of life lost via the unit factors left out of the problem:
    60 min = 1 hr
    24 hr = 1 day
    365 day = 1 year

5. Setup the Dimensional Analysis Sequence:

 
  ??? yrlifelost = 25 yrsmok X 365 daysmok X 1.5 pack X 20 cig X 8 minlost X 1 hrlost X 1 daylost X 1 yrlost = 4.2 yrlifelost  
1 1 1 yrsmok 1 daysmok 1 pack 1 cig 60 minlost 24 hrlost 365 daylost 1