Problem Solving Skills ( ) Lecture 2

Transcription

1 Problem Solving Skills ( ) Lecture 2

2 Puzzle At six o clock in the morning the wall clock struck 6 times and the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 times at noon? Common misconception: as 12 strikes= 2 6 strikes, then 2 30 seconds = 60 seconds. 2

3 Puzzle Graphical representation: Seconds 0 30 Many possible interpretations: Duration

4 Puzzle If we represent: x time for a single stroke y time for a break then 6x + 5y = 30, where x 0 and y 0. 4

5 Rule #1 Rule #1: Be sure you understand the problem, and all the basic terms and expressions used to define it. 5

6 Money and percentages You are buying a car. A dealer offers you two options to choose from: A. You get 15% reduction from the price of the car and then you are charged 10% commission. B. You are charged 10% commission first and then you get 15% reduction. Which option is better for you? Which option is better for the dealer? 6

7 Money and percentages 7

8 Money and percentages A man bought a product with a 20% discount from the marked price and sold it at the price to his friend. What was his profit in % to the price he paid for the product? 8

9 Money and percentages Two girls, Lucy and Jennifer are working in the office. They are paid for every document they prepare. However, for every document she prepares Lucy is paid 10% less than Jennifer but she prepares 10% more documents per day than Jennifer. Who earns more per day? 9

10 Money and percentages 10

11 Averages, again A consultant worked for one company for $60 per hour. Later she worked for another company for $40 per hour. She earned the same amount of money in both jobs. What was her average hourly rate for those two jobs? 11

12 Averages, again 12

13 Averages, again 13

14 Averages, again 14

15 Money and percentages Interest rates has increased from 5% to 7%. What is the percentage increasein the interest rate? 15

16 Money and chances One evening two people won $500 in a business. How much will four people win the following evening? 16

17 Buying cakes Carol bought for a party several bottles of juice at $8 per bottle and several cakes at $11 each. The total cost was $100. How many cakes did she buy? 17

18 Buying cakes 18

19 Diophantine equations The equation 8 b + 11 c = 100 constitutes an example of diophantine equation (named after Diophantus of Alexandria, a famous Greek mathematician of antiquity), in which we have fewer equations than unknowns and the values of the unknowns are restricted to integer values. 19

20 Puzzle One day a customer arrived at a 7-Eleven shop and selected four items. He then approached the counter to pay for these items. The salesman took out his calculator, pressed a few buttons, and said: The total price is $7.11. Why? said the customer, who was amazed by this coincidence. Do I have to pay $7.11 because the name of the shop is 7 Eleven? Of course not! replied the salesman. I have multiplied the prices of these four items and I have given you the result! Why did you multiply these numbers? asked surprised customer. You should have added them to get the total price! Oh, yes, I'm sorry, the salesman said. I have a terrible headache and pressed the wrong button! Then the salesman repeated all the calculations (i.e. he added the prices of these four items), but to both of their great surprise, the total was still $7.11. What are the prices of these four items? 20

21 Diophantine equations We have to solve diophantine equations: x + y + z + t = 711 and xyzt = Enjoy! 21

22 Any Question???