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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."

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."

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?

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?

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!!!

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Fruit Pricing:

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!

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A Roman numerals problem.

1. What number is this? MDCCLXXVI   It is on a famous monument.

2. What Roman numbers of two integers between one and twenty become larger whe the left-hand interger is omitted?

Answer to number 1 is 1776 and number 2 is IV (4) and IX (9).

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Numbers That Ring Bells!

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