Return to the Purplemath home page

 The Purplemath Forums
Helping students gain understanding
and self-confidence in algebra


powered by FreeFind

 

Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

"Percent of" Word Problems:
    General Increase and Decrease Examples 
(page 3 of 3)

Sections: Basic percentage exercises, Markup / markdown, General increase / decrease


Note that, while the values below do not refer to money, the procedures used to solve these problems are otherwise identical to the markup - markdown examples on the previous page.

  • Growing up, you lived in a tiny country village. When you left for college, the population was 840. You recently heard that the population has grown by 5%. What is the present population?

    First, I'll find the actual amount of the increase. Since the increase is five percent of the original, then the increase is:

      (0.05)(840) = 42

    The new population is the old population plus the increase, or:

      840 + 42 = 882

      The population is now 882.

  • Your friend diets and goes from 125 pounds to 110 pounds. What was her percentage weight loss?

    First, I'll find the absolute weight loss:

      125 110 = 15

    This fifteen-pound decrease is some percentage of the original, since the rate of change is always with respect to the original value. So the percentage is "change over original", or:

      15 = (x)(125)

      15 125 = x        (See? The change, 15, is over the original, 125.)

      15 125 = 0.12

    The change is a percentage, so I need to convert this decimal to percentage form:

      She lowered her weight by 12%.

  • Your boss says that his wife has put an 18 51 foot garden in along the whole back end of their back yard. He says that this has reduced the back-yard lawn area by 24%. What are the total dimensions of his back yard? What are the dimensions of the remaining lawn area?   Copyright Elizabeth Stapel 1999-2011 All Rights Reserved

 

ADVERTISEMENT

 

    Since no suburban lot is going to be only eighteen feet wide (because then the house couldn't fit along the street frontage), the width of the lot must be the 51-foot dimension. Now I need to figure out the length of the back yard. The area of the garden is:

      (18)(51) = 918

    This represents 24% of the total yard area; that is, 24% of the original lawn area. This says that (918 square feet) is (twenty-four percent) of (the original), so:

      918 = 0.24x

      918 0.24 = x = 3825

    The total back yard area is 3825 square feet. Since the width is 51 feet, then:

      3825 51 = 75

    The length then is 75 feet. Since 18 feet are taken up by the garden, then the lawn area is 75 18 = 57 feet deep.

      The back yard measures 51' 75' and the lawn measures 51' 57'.

<< Previous  Top  |  1 | 2 | 3  |  Return to Index


(What follows is an aside.)

You may have wondered about the repeated contrast in these pages between "relative" numbers and "absolute" numbers. You should be aware of the difference between the two, because they can be used by those "with an ax to grind" to take exactly the same numbers and come to exactly the opposite conclusions.

For instance, consider the politics of welfare in the United States. I would posit that any family on welfare is a tragedy, and that the legal structure of the economy should be changed to allow more opportunities for advancement. But others with a vested interest in the status quo just squabble over how the present system, and thus their power base, should be expanded. One of their techniques is to argue for more benefits for "their" group, while claiming that "their" group shouldn't be blamed for the problem. How can they do this, when they're using the same statistics each time? They do it by picking and choosing when to use relative numbers versus absolute numbers:

In the United States, those classified as "black" comprise about 12% of the population, while those classified as "white" comprise about 75% of the population. Since "whites" outnumber "blacks" by more than six to one, it is only reasonable that there would be more "whites" on welfare than "blacks" in absolute numbers. That is, when you count them up, there are more "whites" receiving welfare than "blacks", as one would reasonably expect. When certain "leaders" claim that "blacks" aren't the majority of welfare recipients, they are using the absolute numbers.

However, of all welfare recipients, only 50% are "white" (you would expect 75% to be "white") and 35% are "black" (you would expect only 12% to be). In other words, "blacks" are three times more likely to be on welfare than they ought to be, if you just look at their percentage of the population. When certain "leaders" claim that cutbacks to welfare programs are somehow "aimed" at "blacks", because "blacks" will be the ones allegedly hurt, they are using these relative numbers.

Politicians and other charlatans often operate this way: riding both sides of the fence, and changing their interpretations of the numbers to suit the latest money-making opportunities. You should be aware of this two-facedness, and should listen to their arguments while carrying this fact in the back of your head. It'll make you a lot harder to fool. Each interpretation above is correct as far as it goes but you should always wonder what the actual numbers are, what the speaker's motivations are, and whether you have enough information to come to your own independent conclusions.

<< Previous  Top  |  1 | 2 | 3  |  Return to Index

Cite this article as:

Stapel, Elizabeth. "'Percent of' Word Problems: General Increase and Decrease Examples."
    Purplemath. Available from 
http://www.purplemath.com/modules/percntof3.htm.
   Accessed
 

 



Purplemath:
  Linking to this site
  Printing pages
  School licensing


Reviews of
Internet Sites:
   Free Help
   Practice
   Et Cetera

The "Homework
   Guidelines"

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor


This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 1999-2012  Elizabeth Stapel   |   About   |   Terms of Use

 

 Feedback   |   Error?