BOA 501 (Proportions) CRS SKILL BOA 501 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION BOA-­‐ 302 Solve some routine two-­‐step arithmetic problems. BOA 401 Solve routine two-­‐step or three-­‐step problems that involve concepts such as rate and proportion Level 2 – MOST students will BOA 501 Solve multistep arithmetic problems that attain mastery of the focus skill in involve rates, proportions and planning isolation. Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will BOA 601 Solve word problems containing several attain mastery of the extension rates or proportions. skill. Level 1 1. You are putting down hardwood floor in your kitchen. You select an option that is $2.99 per square foot. If your kitchen measures 20 feet by 8 feet, how much will the hardwood cost you? 2. Physics tells us that weights of objects on the moon are proportional to their weights on Earth. Suppose an 180 lb. man weighs 30 lb. on the moon. What will a 60 lb. boy weigh on the moon? 3. Sandy has an 18-­‐foot tall flagpole in her yard. One day for a science project she measures the shadow of the flagpole’s shadow to be 12 feet. If she has a tree in her yard with a 30-­‐foot long shadow how tall is the tree? 1 4. A candy maker put prizes in 600 bags of candy. He then took a random sample of 125 bags of candy and counted 8 bags with prizes in them. Approximately how many bags of candy did the candy maker have? 5. A candy maker estimated that she had 2500 bags of candy. She had put prizes in 92 of them. She collected a sample in which there were 7 bags of candy with prizes. Approximately how many bags of candy were in the sample the candy maker collected? 6. In Physics class the girl to boy ratio is 10 to 4. If there are 20 girls, how many boys are
there?
7. If Annathea earned $250 for 16 hours of work. At this rate how much will she earn for
40 hours of work?
8. In order to determine his pulse rate, Mark counted 16 beats in 15 seconds. At this rate
how many beats would he have in 60 seconds?
2 9. Ralph sold 13 computer games for $112. At this rate, how much would he get for 25 computer games? 10. A biologist tagged 240 perch in Brown’s Lake. Then sometime later, she collected a sample of 80perch, of which 12 were tagged. What is the best estimate for the number of perch in Brow’s Lake? 11. A student can read 7 pages of a book in 10 minutes. How long would you estimate it would take this student to read, Harry Potter and the Prisoner of Azkaban, a book that is 435 pages long? 12. If you had to travel 1360 miles in five days, how many miles would you have to cover in the first three days in order to stay on schedule? 13. In order to pass his final exam, Lars needs to get at least 7 out of every ten questions correct. If he ended up getting 30 questions correct and he passed, what is the minimum number of questions that could have been on the exam? Level 2 14. A room is 16 feet 8 inches long, and the ratio of the width to the length is 4 to 5. What is the width of the room? 3 15. If the ratio of male to female teachers is 1:6 and in 2012 there were 3,700,000 full time teachers in the United States, about how many of them were male? 16. If a team wins 5 games and loses 6, how many would you expect to them to win if they played 45 games? 17. The ratio of boys to girls at a One Direction concert, performed at the Kohl Center, is 3:7. If the Kohl Center in Madison, is at capacity, and has a capacity of 17,230, how many girls were in attendance. 18. A recipe calls for 3 cups of mushrooms. If 1 pound is 5 and ½ cups how many ounces should you buy? Round your answer to the nearest ounce. Note there are 16 ounce in each pound. 19. The table below contains counts of mouth cancer for smokers and non-­‐smokers from a medical center. Smokers Non-­‐Smokers Cancer YES NO 459 11 9 321 Estimate the difference in proportions of those who smoked and had cancer and non-­‐smokers who had cancer. 4 20. It takes Captain Awesome 17.4 minutes to run a 3.6-­‐mile course. If he runs at that same pace, how far could he run in an hour? 21. Shawna reduced the width of a rectangle to 1.5 in. If the proportionality of the dimensions is maintained, what is the new length if it was originally 24 inches long and 9 inches wide? 22. Chuck ate 15 strawberries in 2 minutes and 15 seconds. How long would it take for him to eat 32 strawberries? 23. At a small college, the ratio of men to women is 9:4. If there are presently 720 women, how many additional women would it take to reduce the ratio of men to women to 2:1. 24. a. In Table 1, how many cookies could you make with 2.5 cups of flour? b. In Table 1, how many cups of flour would you need to make 85 cookies? 5 25. A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If there is 64 ounces of cereal, find the amount of rice, wheat and corn. 26. A pound of rye grass seed covers 120 square feet of lawn. How many pounds are needed to seed
a lawn measuring 60 feet by 50 feet? 27. You need new rain gutters on your house. Your directions instruct you that the gutters should decline 0.25 inches for every four feet of rain gutter. The gutters span 37 feet on your house. How much lower than the starting point should the low end be? 28. The ratio of green M & M’s to yellow is 2 : 5. a.
If there are only green and yellow M & M’s in the bag, what is the smallest number of M & M’s possible? b.
If there are 84 M & M’s in the bag all together, how many are green? c.
If red M & M’s were added to the bag in part b to get a total of 100, what is the ratio of green to yellow to red? Level 3 29. If it takes 12 minutes to cut a log into 4 pieces, how many minutes will it take to cut a log into 3 pieces? 6 30. Adam, Chad and David got paid a total of $240 for mowing neighborhood lawns. They split the money in the ratio of 5:9:10. How much less did Adam make than Chad? 31. Adam complained about making so much less. The boys decided to break up their pay in a ratio of 3:4:5 instead. How much more does Adam make than in part a? 32. Jeremy the Sloth can travel at the rate indicated on the graph below. At this rate how many feet will Jeremy travel in one day? 33. Manuela is drawing a map of her local park. The actual park is 500 feet long and 400 feet wide. Manuel needs her drawing to fit on her paper, so she decides to make the long side 10 inches. a. What scale is Manuela using? b. What is the area of her drawing in square inches? 7 34. An I-­‐beam is 12 feet long and weighs 52 pounds. How much does an I-­‐beam of the same width weigh if it is 20 meters long? Level 4 34. Morgana and Kelly have a number of jellybeans in a ratio of 5:3. Kelly and Matthew have a number of jellybeans in a ratio of 6:1. a. What is the ratio of Morgana’s jellybeans to Matthew’s? b. If Morgana and Kelly have 64 jellybeans, how many does Kelly have? c. How many does Matthew have? 33. One piece of pipe 42 meters long is cut into two pieces. The lengths of the pieces are in a ratio of 2:5. What are the lengths of both pieces? 34. The American antelope (pronghorn) and the wildebeest are among the fastest mammals on the planet, particularly at running long distances. The maximum-­‐recorded speed for the antelope is 88.5km/h, which it can sustain for nearly one kilometer. On the other hand, the distance d in kilometers that the wildebeest can run in t hours is given by the equation d=80.5t. Assuming both animals are running at constant speeds, which animal can run faster? 8 35. A rope that is 2 feet and 6 inches long is cut into 3 strips in a ratio of 2:3:5. a. How long is the longest piece? b. How much longer is the longest piece than the shortest one? c. What is the length of each piece if they are cut in a 1:2:3 ratios? 36. It costs 90 cents for The Striped Toothpaste Company to make, package and ship a tube of toothpaste. The company also has "overhead costs" of $3000 per month. The company sells (at wholesale) cartons of toothpaste at the price of $2.50 per tube. This month, the company sold 5000 tubes of toothpaste. What is this month's profit? 37. Jackson and his grandfather constructed a model for a birdhouse. Many of their neighbors offered to buy the birdhouses. Jackson decided that building birdhouses could help him earn money for his summer camp, but he is not sure how long it will take him to fill all of the requests for birdhouses. If Jackson can build 7 birdhouses in 5 hours, write an equation that will allow Jackson to calculate the time it will take him to build any given number of birdhouses. a. Write an equation that you could use to find out how long it will take him to build any number of birdhouses. b. How many birdhouses can Jackson build in 40 hours? c. How long will it take Jackson to build 35 birdhouses? Use the equation from part a to solve the problem. d. How long will it take to build 71 birdhouses? Use the equation from part a to solve the problem. 9 38. The ratio of comedy movies to dramas in Sam’s movie collection is 4:9. If Sam has 169 movies in his collection, how many more comedies would he have to add to make the ratio of his movie collection 1:1? Level 5 39. Three gear wheels, A ,B, and C are in contact. Wheel A has 20 teeth, wheel B has 60 teeth and wheel C has 20 teeth. a. If wheel A is spinning at 60 revolutions per minute, then how fast is wheel B turning in revolutions per minute? b. If wheel A is spinning at 60 revolutions per minute, then how fast is wheel C turning in revolutions per minute? 10 40. There are 600 dishes that need to be rinsed. John can rinse them in 120 minutes by himself. It will take his friend Bob 60 minutes to rinse these dishes. How long will it take them if they rinse these 600 dishes together? 41. Worker A can finish a job in 3 hours. When working at the same time as Worker B, they can finish the job in 2 hours. How long does it take for Worker B to finish the job if he works alone? 41. If Alex can build a house in 2 days and his apprentice Bob can build a house in 3 days, then how long will it take Alex and Bob to build a house when they are working together? 42. Kayla’s chemistry teacher asked her to find the number of atoms in 22 grams of copper. Use the following information to help Kayla out: 63.5 grams of copper = 1 mole of copper 23 1 mole = 6.02 x 10 atoms of copper 43. Last season, the Olympic Women’s Beach Volleyball duo of Misty May and Kerri Walsh won 55 of their games. The ratio of their wins to losses was 5 to 1. This season, the women played the same number of games as last season, but had 8 more wins. What is the ratio of their wins to losses for this season? 11 Mixed Review 42. An archaeologist found four pieces of an ancient circular plate. The first piece is 1/5 of the plate. The second is 1/7th of the plate. The third is 1/5 of the plate. The fourth is 1/6 of the plate. Does the archaeologist have all of the pieces to reconstruct the plate? 43. James built a rectangular banner that is 8 feet long and has an area of 24 square feet. What is the width of James’s banner? 44. You are on a plane flying to Hawaii. You spend 2/3 of your time on the flight reading magazines. You read movie reviews for 2/3 of the time you are reading magazines. What fraction of the whole flight do you spend reading movie reviews? 45. Solve each percentage problem. (round your answers to the nearest hundredth) a. 90% of 95.6 is what? b. 93% of what is 130.7? c. 78 is 92% of what? d. What is 91% of 205.8? e. 78 is what % of 25? 12