Answers to previous problems are down below.
Just scroll down for them. Scroll carefully because the questions come up first, so
if you want to try them before you see the answer, don't scroll all the way down.

This problem was taken from the magazine: Mathematics
Teaching in the Middle School. January 1999.

Prepared by DAVID SPANGLER,
david.spangler@aw.com. Spangle teaches at National-Louis
University Evanston, IL 60201. He is also an editorial manager for a textbook
publishing company and is always looking for ways to teach mathematics through engaging,
real world applications.

SOMETHING IS WRONG WITH EACH OF THE advertisements to the right. Are the mistakes
honest errors ... or is someone trying to "pull the wool over our eyes"?
Sometimes it is hard to tell for sure. But we can put on our detective hat to investigate
what these advertisements are saying mathematically. The questions that follow will help
us determine whether the bananas are "a-peeling," whether the lamps are a
"shady" deal, and whether the CDs should be "music to your ears."

Questions Advertisement 1

1. For advertisement 1 how much money is .49¢?

a) 49 cents
b) $0.49 c) about a half cents

d)$O.049 e) S0.0049

2. Explain whether a customer would be mathematically
correct in telling the clerk, "I'd like to buy two pounds of bananas. Here is one
cent. You can keep the change."

3. How would you correct advertisement 1?

Advertisement
2

4. For advertisement 2, let us consider this situation.
Suppose that a lamp regularly sells for $120.

a) What would the lamp cost after a first
discount of 60 percent is applied?

b) What would the lamp cost after the second discount, 25
percent, is applied to the discounted price in question 4a?

c) How much money would you save with the two discounts? The total
dollar savings is what percent of the original selling price?

d) How did the advertising agent arrive at 85 percent? How would
you explain to him or her why this amount is incorrect?

Advertisement 3

5. In advertisement
3, how much would a CD cost if it was discounted at "only" 100 percent off the
list price?

6. What is the correct percent discount
for the CDs? Round your answer to the nearest tenth of a percent.

7. If a CD really sold at 714 percent off
the list price, how much would the store have to pay you if you "bought" the CD?

Here is a chance for you to
become a mathematics detective in your neighborhood. Hunt for misleading or mathematically
incorrect advertisements. Such advertisements may be found in newspapers, direct mail
promotions, on television, in stores, and so on. Bring them to class for discussion. Then
send your favorites to the address that follows. Selected advertisements will be the topic
of a future "Mathematics Detective" article. Copies or descriptions of the
advertisements are sufficient when actual advertisements cannot be sent. Send
advertisements to me by email or by snail mail (regular mail). If you are one of my
students bring them into school. (1point extra credit for
each with explanation of what's wrong.)hbwmathman@oocities.com

Answers for Ad #1:
1) c and e. The
amount .49¢ is
forty-nine hundreths of one cent. 2) The customer would be correct, for
a pound would cost $0.0098, or 98 hundreths of one cent. 3) The price should be
marked as either 49¢/lb or $0.49/ lbs.

Answers for Ad #2:
4a) 60% would be .60 x 120 or $72 so $120 - $72 = $48. 4b) When the second discount
is applied to the now $48 an additional .25 x $48 or $12 is deducted, so $48 - 12 =
$36. 4c) Since the final price is $36, a customer is saving $120 -$36 or $84.
This would be 84/120 ( / means divide) or 70% savings. 4d) The advertising
agent added the two percents. Of course he is wrong!!! One must calculate each
percent separately and in order.

Answers for Ad #3:
5) At 100% the CD would be free!!! 6) The savings would be $13.95 - $3.99, or $9.96. The
percent savings is 9.96/ 13.95 or 0.71397... or about 71.4% 7) This one is very
cool... At 714% off the store would owe you money. The first 100% would take it down
to $0 and the remaining 614% would be 6.14 x 13.95 or about $85.65. That's how
much they would have to pay YOU!!!

Mrs. Hamilton went to her favorite produce
market. An apple
cost 20¢, a strawberry
cost 40¢, and an avocado
cost 28¢. Mrs. Hamilton was hungry for a banana,
but she had only a quarter
in her pocket. Using the same pricing logic, did Mrs. Hamilton have enough money for a banana

The answer is YES she has enough money. Each letter is worth 4¢. So a banana cost
24¢ because there are 6 letters. She would have 1¢ left over. Yeah, Mrs. Hamilton!

This problem is of a different sort. Do these numbers ring a bell?
Well tell me what each one means. For example, 365 can only mean one thing: the
number of days in a year. How many can you get????(Every
3 will be one extra credit point. Max of 4 points for this
week.)

1) 1776 2) 2,000
3) 1.06
4) 2.54

5) 3.1415... 6) 366
7) 1492
8) 0.62

9) 52
10) 360 11) 90
12) 88

Answers: 1)
Signing of Declaration. 2)
pounds in a ton 3)liters in a
quart (approx) 4) centimeter per
inch 5) the number pi 6) days in a leap year 7) Columbus sailed the ocean blue