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