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 dont 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
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