# Figuring Percentages Abstractly and Methodically Too

The word problem I liked from either one of my trusty text books or a website and that I bring each time to lessons describes a \$400.00 flute in a music store that has a 10% discount on it. Then there is a back-to-school sale at which time 15% is taken off of the discounted price of the flute. The girl buys the flute and for which price?
A. 270.00
B. 300.00
C. 306.00
D. 375.00
E. 389.00
An algebraic equation can be used to solve this problem and so can an abstract almost mental method.
Let's start with the latter, the abstract way. 10% of 400.00 is 40.00. Novices might say that deducting another 10% (40.00 dollars more) plus 5% (20.00) would mean that the 400.00 flute cost the buyer 300.00. This would make B the choice of the novice. Yet! What the novice will have missed is that the 10% and 5% (15%) is calculated from \$400.00 minus the initial \$40.00 making \$360.00 the price of the flute at the time of the back-to-school sale. 10% of \$360.00 is \$36.00 and 5% more is 1/2 of the \$36.00, thus \$18.00. \$36.00 plus \$18.00 is \$54.00 and once that amount is deducted from \$360.00, the flute costs \$306.00. Harrowing is it if you consider where you might make this miscalculation and for whom.
The methodical or textbook standard way that you might recall once in an exam room is 400-.10(400) = x and .15(x) = c, the cost of the flute. You will get \$400 - \$40 so \$360 and multiplied times .15 gets you \$54.00. Remember that the initial price was 10% off of \$400.00 so \$360.00, the discounted price, is the number from which we subtract \$54.00. We get \$306.00 again as our answer.
To make this lesson interesting to my student, I drew a flute on a table and hung discount percentage signs on it that looked just like those at our local New Orleans department store, Stein-Mart. The picture was accompanied by my explanation and so that her lesson would be engrossing as well as the parts of the percentages topic and "discounted price" memorable.

\$30p/h

Carol E.

Skilled Math, Test Prep, Reading, and Writing Tutor

1750+ hours
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