WARM-UP SOLVING PROBLEMS

Transcription

1 WARM-UP SOLVING PROBLEMS USING PERCENTS Ex.1) 85% of 440 guests is how many guests? Ex2.) 42 students is 70% of how many students? Ex3.) 576 meals is what percent of 1440 meals? 1-3

2 SOLUTIONS: SOLVING PROBLEMS USING PERCENTS Thus, 374 is 85% of

3 Ch. 2.3 Proportions & Measurement Systems Learning Intentions: Review the English measurement system & the metric system. Convert measurement units using conversion factors. Convert measurement units using dimensional analysis. Learn & use the term rate. 5

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6 EVERYDAY CONVERSION FACTORS What are some conversion factors that you are familiar with? Feet per mile? Seconds per minute? Minutes per day? Centimeters per inch? Check your planners! 1-8

7 EVERYDAY CONVERSION FACTORS What are some conversion factors that you are familiar with? Feet per mile? 5,280ft/1mile Seconds per minute? 60sec/1min Centimeters per inch? 2.54cm/1in. Minutes per day? 1,440min/1day Check your planners! 1-9

8 CONVERTING FROM CENTIMETERS TO INCHES Using the relationship that 1 inch = 2.54 centimeters convert the following measurements from unit into the other centimeters = 2. 1 centimeter = 3. How many centimeters high is a doorway that measures 80 inches? 1-10

9 CONVERTING FROM CM. S TO IN. S 1-11

10 USING CONVERSION FACTORS TO SOLVE PROBLEMS Jonas drove his car from Montana to Canada on vacation. While there, he heeded to buy gasoline and noticed that it was sold by the liter rather than by the gallon. Use the conversion factor 1 gallon = 3.79 liters to determine how many liters will fill his 12.5-gallon gas tank. 1-12

11 USING CONVERSION FACTORS TO SOLVE PROBLEMS 1-13

12 2.3 PROPORTIONS & MEASUREMENT SYSTEMS DAY 2 USING CONVERSION FACTORS TO SOLVE PROBLEMS A radio-controlled car traveled 30 feet across the classroom in 1.6 seconds. How fast was it traveling in miles per hour? 1-14

13 USING CONVERSION FACTORS TO SOLVE PROBLEMS 1-15

14 USING CONVERSION FACTORS TO SOLVE PROBLEMS In 2001, Alan Webb broke Jim Ryun s 36-year-old high school mile record by running 1 mile in 3 minutes seconds. How fast was this in feet per second? 1-16

15 USING CONVERSION FACTORS TO SOLVE PROBLEMS 1-17

16 USE DIMENSIONAL ANALYSIS TO ANSWER THE COMPLETE THE FOLLOWING CONVERSIONS meters per second to kilometers per hour day to seconds ounces to tons (16 oz. = 1 lb; 2000 lb = 1 ton) 1-18

17 USE DIMENSIONAL ANALYSIS TO ANSWER THE COMPLETE THE FOLLOWING CONVERSIONS. 1-19

18 USE DIMENSIONAL ANALYSIS TO ANSWER THE FOLLOWING QUESTION. Which is longer a 1-mile race or a 1500-meter race? Use mathematics to show your reasoning. 1-20

19 USE DIMENSIONAL ANALYSIS TO ANSWER THE FOLLOWING QUESTION. 1-21

20 METRIC TO U.S. CUSTOMARY 1 meter = 3.28 feet 1 kilometer = miles 400 meter dash = miles 0.25 mile 800 meters = miles 0.5 miles 1 meter = 100 cm = 1,000 millimeters 1 kilometer = 1,000 meters 1 foot = 12 inches 1 yard = 36 in. = 3 ft. 1 mile = 5,280 feet = 1,760 yds. 1-22

21 METRIC LIQUID US

22 Percentage Problem You purchased a video game costing $ You used two coupons when buying the video game. The first coupon gives 25% off of the price. The second coupon is for $5.00 off the price of any game. When the clerk rings up your purchase, he takes the $5.00 off first and then applies the 25% discount. Would the price that you paid for the video game have increased, decreased, or stayed the same if the clerk had taken off the 25% discount first and then taken off the $5.00 coupon? Show all work & prove your answer. Two Compliments & a Wish **Pass your index card back one. In a contrasting color to your classmate s original work, write two good things they wrote down & 1 suggestion for solving / making their calculation or proof better. 1-24

23 SOLUTION: Percentage Problem You purchased a video game costing $ You used two coupons when buying the video game. The first coupon gives 25% off of the price. The second coupon is for $5.00 off the price of any game. When the clerk rings up your purchase, he takes the $5.00 off first and then applies the 25% discount. Would the price that you paid for the video game have increased, decreased, or stayed the same if the clerk had taken off the 25% discount first and then taken off the $5.00 coupon? Show all work & prove your answer. Let a = price after $5 off coupon a = 45 5 a = 40 Let b = price after $5 off, then 25% off coupon = b 40 ( 40 1 ) = b 40 (40 1 ) 30 = b Let x = price after 25% off coupon = x 45 ( 45 ) 75 = x (45) = x Let y = price after 25% off, then $5 coupon y = y = Thus, you would have saved $1.25 more with the 25% then $5 off coupon. 1-25