Applications in General

Word problems are the real heart of any higher-level mathematics.  Algebra is no exception!  Why would anyone bother to learn how to solve equations, if the goal were not to solve a real problem, i.e. a word problem?  To solve a word problem, first identify what the problem is asking you to find.  Let that unknown be represented by a variable.  If there is more than one unknown, let the unknown that you know the least about be represented by the variable, and the other unknown be in direct relationship to the variable.


      
Mother bought a bag of candy at the store that contained 55 pieces.  She gave Mary 5 less
       than twice the amount of candy that she gave Tom.  How many pieces of candy did she give
       Mary and Tom?

OK, take a deep breath and begin … what is the problem asking you to find? … how much candy Mary and Tom were given … which do you know the least about? … how much candy Tom was given (since it says that Mary was given 5 less than twice the amount that Tom was given) … if we let the amount of candy Tom was given = , then the amount of candy Mary was given would be five less than twice the amount of Tom’s () … this would look like .  So to “recap”, we have defined our variables….

Amount of candy for Tom =

            Amount of candy for Mary =

Now it says that Mother bought a bag of 55 pieces.  So the sum of Tom’s and Mary’s candy must total 55.  We would then build our equation and solve …

 +  = 55          …form the equation

                  …Collect

                       …Addition

               *          …Division

Tom = , Tom received 20 pieces of candy

Mary = , Mary received  pieces of candy

Now, the argument with application problems that you may give is that “this problem could have been figured that out without algebra!”  This may be true since this problem involved whole numbers.  Many students learned the beginnings of algebra using “guess and test.”  In my opinion, this was unfortunate.  The world does not operate on whole numbers!  Check out your bills at home and the daily purchases that you make.  How often do they end up being “whole” numbers?  At the end of the day, the money in my billfold usually ends up being something like $8.57 … decimals!

       Think about the same problem as above, only Mother purchased 60 candy bars (which could
       be divided, if needed).

Amount of candy for Tom =

Amount of candy for Mary =

 +  = 60          …form the equation

                  …Collect

                       …Addition

                      …Division

Tom = , Tom received  pieces of candy

Mary = , Mary received  pieces of candy

In any application problem the clue is to read the problem carefully … often several times, so that you can identify what type of problem it is and begin a strategy to solve the problem.  Identify what the problem is asking you to find and designate a variable to represent this unknown.  If you have two unknowns then you can only have one variable, usually the quantity that you know the least about.  Any other unknowns are identified using the variable that you designated for the least known quantity.  Next, organize the information that is given to you … diagrams and charts are organizational tools.  Set up an equation that represents the problem and then solve the equation.  Make sure that you have answered the question or questions posed in the problem including units of measure.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 09-Jan-2014