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Notes on Percent by proportion (word problems)


It is often helpful to use the following wording:

    instead of   (they are really the same thing!)


See the following word problems:


1)    A store normally sells a coat for $150.  It is having a 22% off sale.  What is the amount of savings?  What will the coat cost now?

It is easier to look at this problem as part of a whole.  The whole coat costs $150, I don’t know the “part” or discount, so that will be my variable.  I know the percent, plug in the numbers!

           then solve by proportion.

          100n = 3300

100                  100

     n  =  33     $33 is the discount, savings. 

So 150-33 = $117 is the  sales price of the coat.


Whenever you see the word Rate – that is the percent portion of the problem.


I have outlined some common percent words and which part of the problem they refer to.


Discount – part                                        Tax - part              

Discount rate – percent                           Discount rate - percent

Sales       -  whole                                    Sales               - whole


Commission  - part                                  Interest – part

Commission rate – percent                    Interest rate – percent

Sales        -  whole                                   Principal          - whole


Tip     -  part

Tip rate – percent

Food Cost - whole