Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 1 (September 2, 1998)
Topic: Percentages (%'s)

Percentage is a very basic and important topic. Use of percentages occurs
frequently in our daily lives. 

To say that 53 is 6% more than 50 means that 

      53-50    3
      ----- = --- = .06 = 6%.
       50      50

While 53 is 6% more than 50, 50 is not 6% less than 53. To find
what percentage 50 is less than 53, one calculates:

     50-53   -3
     ----- = --- = -.0566 (to 4 decimal places) = -5.66%.
      53     53

So 50 is 5.66% less (the minus sign!) than 53.

                    PROBLEMS
1. Page 15&16 of Text: All of them.

2. Suppose the U.S. population was 266 million in 1996. If the
population increased by 3% from 1995 to 1996, and also by 3%
from 1996 to 1997, what were the populations in 1995 and in 1997?

3. A store marks up coats by 40% above cost and sells them for $60.
  a. What is the cost of the coats to the store? What is the profit?
  b. What percentage of the cost is the profit?
  c. What percentage of the selling price is the profit?
  d. What should the selling price be if the store wanted to
     make a profit of 50% of the selling price (i.e. 50% of what
     it takes in is profit)?

4. A sweater in a certain store has a list price of $60.
  a. If the price is reduced by 15%, what is the 'sale' price?
  b. If the original mark up (over cost) of the store was
      20%, what percentage mark up is the sale price?
  c. Suppose sales continue to lag, and the store advertises
     'Take an additional 10% off the reduced price.' 
     (i)  What is the new price of the sweater?
     (ii) What is the percentage reduction of the original
           list price?

5. Another store sells T-shirts at a 25% mark up. What percentage
of the selling price is the profit?