Exercises
In Exercises 1-12, which of the following is a true proportion?
1. (frac{9}{7} = frac{27}{21}, ~ frac{4}{3} = frac{9}{7}, ~ frac{7}{2} = frac{8}{9}, ~ frac{4}{8} = frac{9}{6})
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2. (frac{6}{7} = frac{18}{21}, ~ frac{2}{3} = frac{8}{6}, ~ frac{4}{3} = frac{3}{2}, ~ frac{8}{9} = frac{3}{8})
3. (frac{7}{6} = frac{28}{24}, ~ frac{5}{6} = frac{5}{4}, ~ frac{9}{5} = frac{7}{3}, ~ frac{9}{2} = frac{8}{9})
4. (frac{7}{6} = frac{2}{8}, ~ frac{4}{5} = frac{5}{7}, ~ frac{3}{4} = frac{15}{20}, ~ frac{8}{4} = frac{8}{7})
5. (frac{6}{5} = frac{24}{20}, ~ frac{7}{3} = frac{2}{4}, ~ frac{2}{4} = frac{2}{6}, ~ frac{5}{2} = frac{2}{8})
6. (frac{9}{8} = frac{4}{3}, ~ frac{5}{7} = frac{10}{14}, ~ frac{8}{6} = frac{5}{4}, ~ frac{8}{5} = frac{2}{6})
7. (frac{3}{5} = frac{2}{8}, ~ frac{3}{7} = frac{6}{14}, ~ frac{5}{6} = frac{2}{4}, ~ frac{7}{4} = frac{5}{9})
8. (frac{7}{3} = frac{7}{6}, ~ frac{4}{7} = frac{8}{14}, ~ frac{5}{3} = frac{7}{8}, ~ frac{5}{7} = frac{6}{9})
9. (frac{5}{4} = frac{25}{20}, ~ frac{9}{3} = frac{9}{6}, ~ frac{7}{4} = frac{3}{6}, ~ frac{3}{5} = frac{9}{4})
10. (frac{7}{6} = frac{6}{9}, ~ frac{7}{3} = frac{2}{5}, ~ frac{6}{7} = frac{30}{35}, ~ frac{4}{7} = frac{2}{8})
11. (frac{9}{7} = frac{4}{3}, ~ frac{9}{4} = frac{7}{9}, ~ frac{3}{5} = frac{6}{10}, ~ frac{3}{9} = frac{9}{5})
12. (frac{4}{3} = frac{8}{7}, ~ frac{2}{6} = frac{5}{8}, ~ frac{7}{2} = frac{3}{6}, ~ frac{9}{4} = frac{36}{16})
In Exercises 13-36, solve the given proportion.
13. (frac{17}{3} = frac{x}{18})
14. (frac{16}{5} = frac{x}{20})
15. (frac{6x + 10}{6} = frac{11}{3})
16. (frac{4x + 8}{12} = frac{5}{3})
17. (frac{17}{9} = frac{x}{18})
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18. (frac{8}{9} = frac{x}{18})
19. (frac{11}{2} = frac{x}{8})
20. (frac{11}{4} = frac{x}{8})
21. (frac{7x + 15}{15} = frac{10}{3})
22. (frac{7x + 3}{8} = frac{5}{4})
23. (frac{11}{2} = frac{x}{10})
24. (frac{19}{6} = frac{x}{18})
25. (frac{5x + 8}{12} = frac{2}{3})
26. (frac{3x + 12}{6} = frac{3}{2})
27. (frac{2}{15} = frac{24}{x})
28. (frac{7}{8} = frac{14}{x})
29. (frac{3}{16} = frac{6}{x})
30. (frac{4}{21} = frac{12}{x})
31. (frac{5}{22} = frac{20}{x})
32. (frac{3}{22} = frac{21}{x})
33. (frac{2x + 10}{6} = frac{14}{3})
34. (frac{2x + 9}{9} = frac{13}{3})
35. (frac{7}{2} = frac{21}{x})
36. (frac{2}{15} = frac{18}{x})
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37. If 13 dog bones cost $1.97, what will be the cost for 7 dog bones (assuming an equal rate)? Round your answer to the nearest penny.
38. If 2 watermelons cost $3.89, what will be the cost for 11 watermelons (assuming an equal rate)? Round your answer to the nearest penny.
39. If 7 bananas cost $2.55, what will be the cost for 14 bananas (assuming an equal rate)? Round your answer to the nearest penny.
40. If 2 apples cost $2.05, what will be the cost for 8 apples (assuming an equal rate)? Round your answer to the nearest penny.
41. If 13 oranges cost $3.61, what will be the cost for 11 oranges (assuming an equal rate)? Round your answer to the nearest penny.
42. If 3 watermelons cost $1.05, what will be the cost for 9 watermelons (assuming an equal rate)? Round your answer to the nearest penny.
43. If 3 dog bones cost $1.23, what will be the cost for 13 dog bones (assuming an equal rate)? Round your answer to the nearest penny.
44. If 3 watermelons cost $4.41, what will be the cost for 7 watermelons (assuming an equal rate)? Round your answer to the nearest penny.
45. If 3 apples cost $3.24, what will be the cost for 13 apples (assuming an equal rate)? Round your answer to the nearest penny.
46. If 6 apples cost $3.43, what will be the cost for 7 apples (assuming an equal rate)? Round your answer to the nearest penny.
47. If 4 dog bones cost $1.03, what will be the cost for 8 dog bones (assuming an equal rate)? Round your answer to the nearest penny.
48. If 4 oranges cost $4.28, what will be the cost for 3 oranges (assuming an equal rate)? Round your answer to the nearest penny.
49. Two rolls. In Haiti, two flat rolls cost 5 gourdes, about 12 cents. How many cents would 20 rolls cost? Associated Press-Times-Standard 02/18/10 Haiti’s earthquake camps turning into shanty towns.
50. Turbines. As proposed, the Shell Wind Energy project consists of 25 ridge-top turbines that can generate up to 50 megawatts, or enough to supply electricity to about 1, 000 homes. Estimate the number of ridge-top turbines that would be needed to supply electricity to 70, 000 homes, the approximate number of properties in Humboldt County, CA. John Driscoll Times-Standard 12/24/09 Wind power project goes under analysis.
51. Dumptrucks. U.S. Highway 199 had a landslide where as much as 3, 000 cubic yards of material fell on the road, reportedly requiring about 200 large dumptrucks to remove. Only a week earlier, 40, 000 cubic yards of material fell on Highway 96. Estimate the number of dumptrucks needed for that slide rounded to the nearest whole number. Associated Press-Times-Standard 03/09/10 Another highway closed by slide.
52. Timber sales. Alaska’s 26, 000 square mile Tongass National Forest plan allows for timber sales of up to 267 million board-feet per year – enough for nearly 27, 000 two-bedroom homes, but demand for timber is far short of that. Less than 25 million board-feet was logged in the forest in 2009. Forest Service officials have said they hope to increase logging in the Tongass to about 100 million board-feet per year. Associated Press-Times-Standard 02/18/10 Industry loses lawsuit over logging in Alaska.
i) Estimate the number of 2-bedroom homes that 25 million board-feet of timber would build.
ii) How many 2-bedroom homes would 100 million board-feet of timber build?
53. Costly spill. In Australia, penalties on ships causing oil spills are approximately $1.75 million Australian dollars, equivalent to about $1.64 million US dollars. After an oil tanker was grounded onto a coral reef, Australian officials are considering raising the fine to $10 million Australian dollars. What will the new fine be in US dollars? Round your answer to the nearest hundredth of a million dollars. Associated Press-Times-Standard 04/13/10 Ship that leaked oil on Great Barrier Reef removed.
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