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1.5 Exercise Set

Solve.

1. $4 x + 5 = 21$ $4 x + 5 = 21$
2. $2 y - 1 = 3$ $2 y - 1 = 3$
3. $23 - \frac{2}{5} x = - \frac{2}{5} x + 23$ $23 - \frac{2}{5} x = - \frac{2}{5} x + 23$
4. $\frac{6}{5} y + 3 = \frac{3}{10}$ $\frac{6}{5} y + 3 = \frac{3}{10}$
5. $4 x + 3 = 0$ $4 x + 3 = 0$
6. $3 x - 16 = 0$ $3 x - 16 = 0$
7. $3 - x = 12$ $3 - x = 12$
8. $4 - x = - 5$ $4 - x = - 5$
9. $3 - \frac{1}{4} x = \frac{3}{2}$ $3 - \frac{1}{4} x = \frac{3}{2}$
10. $10 x - 3 = 8 + 10 x$ $10 x - 3 = 8 + 10 x$
11. $\frac{2}{11} - 4 x = - 4 x + \frac{9}{11}$ $\frac{2}{11} - 4 x = - 4 x + \frac{9}{11}$
12. $8 - \frac{2}{9} x = \frac{5}{6}$ $8 - \frac{2}{9} x = \frac{5}{6}$
13. $8 = 5 x - 3$ $8 = 5 x - 3$
14. $9 = 4 x - 8$ $9 = 4 x - 8$
15. $\frac{2}{5} y - 2 = \frac{1}{3}$ $\frac{2}{5} y - 2 = \frac{1}{3}$
16. $- x + 1 = 1 - x$ $- x + 1 = 1 - x$
17. $y + 1 = 2 y - 7$ $y + 1 = 2 y - 7$
18. $5 - 4 x = x - 13$ $5 - 4 x = x - 13$
19. $2 x + 7 = x + 3$ $2 x + 7 = x + 3$
20. $5 x - 4 = 2 x + 5$ $5 x - 4 = 2 x + 5$
21. $3 x - 5 = 2 x + 1$ $3 x - 5 = 2 x + 1$
22. $4 x + 3 = 2 x - 7$ $4 x + 3 = 2 x - 7$
23. $4 x - 5 = 7 x - 2$ $4 x - 5 = 7 x - 2$
24. $5 x + 1 = 9 x - 7$ $5 x + 1 = 9 x - 7$
25. $5 x - 2 + 3 x = 2 x + 6 - 4 x$ $5 x - 2 + 3 x = 2 x + 6 - 4 x$
26. $5 x - 17 - 2 x = 6 x - 1 - x$ $5 x - 17 - 2 x = 6 x - 1 - x$
27. $7 (3 x + 6) = 11 - (x + 2)$ $7 (3 x + 6) = 11 - (x + 2)$
28. $4 (5 y + 3) = 3 (2 y - 5)$ $4 (5 y + 3) = 3 (2 y - 5)$
29. $3 (x + 1) = 5 - 2 (3 x + 4)$ $3 (x + 1) = 5 - 2 (3 x + 4)$
30. $4 (3 x + 2) - 7 = 3 (x - 2)$ $4 (3 x + 2) - 7 = 3 (x - 2)$
31. $2 (x - 4) = 3 - 5 (2 x + 1)$ $2 (x - 4) = 3 - 5 (2 x + 1)$
32. $3 (2 x - 5) + 4 = 2 (4 x + 3)$ $3 (2 x - 5) + 4 = 2 (4 x + 3)$
33. New Words in the English Language. During the nineteenth century, 75,029 new words entered the English language. This is about 46.9% more than the number of new words in the seventeenth century. (Source: Philip Durkin and Katherine Martin, Oxford University Press; “English by the Book,” National Geographic, December 2013) Find the number of new words that appeared in the English language in the seventeenth century.
34. Calorie Intake. The average worldwide daily calorie intake per person has increased from 2200 to 2800 calories since the early 1960s. The average daily calorie intake per person in the United States is 3688. This is about 86.4% more than the average daily calorie intake per person in Haiti. (Sources: UN Food and Agriculture Organization; World Health Organization) Find the average daily calorie intake per person in Haiti.
35. Amount Borrowed. Kea borrowed money from her father at 5% simple interest to help pay her tuition at Wellington Community College. At the end of 1 year, she owed a total of $1365 in principal and interest. How much did she borrow?
36. Amount of an Investment. Khalid makes an investment at 4% simple interest. At the end of 1 year, the total value of the investment is $1560. How much was originally invested?
37. Angle Measure. In triangle ABC, angle B is five times as large as angle A. The measure of angle C is $2^{°}$ $2^{°}$ less than that of angle A. Find the measures of the angles. (Hint: The sum of the angle measures is $180^{°}$ $180^{°}$ .)
38. Angle Measure. In triangle ABC, angle B is twice as large as angle A. Angle C measures $20^{°}$ $20^{°}$ more than angle A. Find the measures of the angles.
39. Clothing Trade Deficit. Imports of clothing to the United States totaled $84.916 billion in 2012. This amount was $1.459 billion less than twenty-five times the clothing exports that year. (Source: Bureau of Economic Analysis, U.S. Department of Commerce) Find the amount of clothing exports from the United States in 2012.
40. Foreign Trade. In 2012, the total value of exports from the United States was $2,210,585,000,000. That year, exports were $837,965,000,000 more than half of the U.S. imports. (Source: U.S. Bureau of Economic Analysis, U.S. Department of Commerce) Find the value of imports to the United States in 2012.
41. Train Speeds. A Central Railway freight train leaves a station and travels due north at a speed of 60 mph. One hour later, an Amtrak passenger train leaves the same station and travels due north on a parallel track at a speed of 80 mph. How long will it take the passenger train to overtake the freight train?
42. Distance Traveled. A private airplane leaves Midway Airport and flies due east at a speed of 180 $k m / h$ $k m / h$ . Two hours later, a jet leaves Midway and flies due east at a speed of 900 $k m / h$ $k m / h$ . How far from the airport will the jet overtake the private plane?
43. Income Taxes. In 2010, 40.9% of federal tax returns had zero or negative tax liability. This amount is 15.7% more than the percentage of filers who had zero or negative tax liability in 2000. (Source: The Tax Foundation) Find the percentage of tax filers in 2000 who had zero or negative tax liability.
44. Salary Comparison. The average annual salary of a restaurant manager is 24.8% less than the average annual salary of an office manager. The average annual salary of a restaurant manager is $48,533. (Source: www.salary.com) Find the average annual salary of an office manager.
45. Commission vs. Salary. Juliet has a choice between receiving a monthly salary of $1800 from Furniture by Design or a base salary of $1600 and a 4% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal?
46. Sales Commission. Edward, a consumer electronics salesperson, earns a base salary of $1270 per month and a commission of 6% on the amount of sales he makes. One month Edward received a paycheck for $3154. Find the amount of his sales for the month.
47. Studying Abroad. In the 2012–2013 school year, approximately 820,000 foreign students studied in the United States. The number of U.S. students who studied abroad that same year was about seven-twentieths of the number of foreign students who studied in the United States. (Source: Pew Research Center) Find the number of U.S. students who studied abroad during the 2012–2013 school year.
48. Population Density. The population density in China is 365.3 persons per square mile. The population density in the United States is approximately one-fourth of the density in China. (Source: The World Almanac 2014) Find the population density in the United States.
49. Soccer-Field Dimensions. The width of the soccer field recommended for players under the age of 12 is 35 yd less than the length. The perimeter of the field is 330 yd. (Source: U.S. Youth Soccer) Find the dimensions of the field.
50. Poster Dimensions. Marissa is designing a poster to promote the Talbot Street Art Fair. The width of the poster will be two-thirds of its height, and its perimeter will be 100 in. Find the dimensions of the poster.
51. Test-Plot Dimensions. Morgan’s Seeds has a rectangular test plot with a perimeter of 322 m. The length is 25 m more than the width. Find the dimensions of the plot.
52. Garden Dimensions. The children at Tiny Tots Day Care plant a rectangular vegetable garden with a perimeter of 39 m. The length is twice the width. Find the dimensions of the garden.
53. Flying into a Headwind. An airplane that travels 450 mph in still air encounters a 30-mph headwind. How long will it take the plane to travel 1050 mi into the wind?
54. Flying with a Tailwind. An airplane that can travel 375 mph in still air is flying with a 25-mph tailwind. How long will it take the plane to travel 700 mi with the wind?
55. Investment Income. Katie invested a total of $5000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $176 interest. How much was invested at each rate?
56. Student Loans. Anton’s two student loans total $9000. One loan is at 5% simple interest and the other is at 6% simple interest. At the end of 1 year, Anton owes $492 in interest. What is the amount of each loan?
57. Patents. In 2013, IBM (International Business Machines) received 2133 more patents than Samsung. Together, they received 11,485 patents. (Source: IFI Claims Patent Services) How many patents did each company receive?
58. Books about Presidents. There are 5493 print and e-books written about both George Washington and Abraham Lincoln. There are 1675 more books about Lincoln than about Washington. (Source: Bowker Books in Print) How many books have been written about each president?
59. Ocean Depth. The average depth of the Pacific Ocean is 14,040 ft, and its depth is 8890 ft less than the sum of the average depths of the Atlantic and Indian Oceans. The average depth of the Indian Ocean is 272 ft less than four-fifths of the average depth of the Atlantic Ocean. (Source: Time Almanac 2010) Find the average depth of the Indian Ocean.
60. Calcium Content of Foods. Together, one 8-oz serving of plain nonfat yogurt and one 1-oz serving of Swiss cheese contain 676 mg of calcium. The yogurt contains 4 mg more than twice the calcium in the cheese. (Source: U.S. Department of Agriculture) Find the calcium content of each food.
61. Water Weight. Water accounts for 55% of a woman’s weight (Source: ga.water.usgs.gov/edu). Lily weighs 135 lb. How much of her body weight is water?
62. Water Weight. Water accounts for 60% of a man’s weight (Source: ga.water.usgs.gov/edu). Jake weighs 186 lb. How much of his body weight is water?
63. Traveling Upstream. A kayak moves at a rate of 12 mph in still water. If the river’s current flows at a rate of 4 mph, how long does it take the boat to travel 36 mi upstream?
64. Traveling Downstream. Angelo’s kayak travels 14 km/h in still water. If the river’s current flows at a rate of 2 km/h, how long will it take him to travel 20 km downstream?
65. Hourly Wage. Rosalyn worked 48 hr one week and earned a $1066 paycheck. She earns time and a half (1.5 times her regular hourly wage) for the number of hours she works in excess of 40. What is Rosalyn’s regular hourly wage?
66. Cab Fare. City Cabs charges a $1.75 pickup fee and $1.50 per mile traveled. Diego’s fare for a cross-town cab ride is $19.75. How far did he travel in the cab?
67. Olive Oil. Together, Italy, Spain, and the United States consume 58% of the world’s olive oil. The percentage consumed in Italy is $3 \frac{3}{4}$ $3 \frac{3}{4}$ times the percentage consumed in the United States. The percentage consumed in Spain is $\frac{2}{3}$ $\frac{2}{3}$ of the percentage consumed in Italy. (Source: www.OliveOilEmporium.com) Find the percent of the world’s olive oil consumed in each country.
68. NFL Stadium Elevation. The elevations of the 31 NFL stadiums range from 3 ft at Mercedes-Benz Superdome, New Orleans, Louisiana, to 5280 ft at Sports Authority Field at Mile High, Denver, Colorado. The elevation of Sports Authority Field at Mile High is 275 ft higher than seven times the elevation of Lucas Oil Stadium in Indianapolis, Indiana. What is the elevation of Lucas Oil Stadium?

Find the zero of the linear function.

69. $f (x) = x + 5$ $f (x) = x + 5$
70. $f (x) = 5 x + 20$ $f (x) = 5 x + 20$
71. $f (x) = - 2 x + 11$ $f (x) = - 2 x + 11$
72. $f (x) = 8 + x$ $f (x) = 8 + x$
73. $f (x) = 16 - x$ $f (x) = 16 - x$
74. $f (x) = - 2 x + 7$ $f (x) = - 2 x + 7$
75. $f (x) = x + 12$ $f (x) = x + 12$
76. $f (x) = 8 x + 2$ $f (x) = 8 x + 2$
77. $f (x) = - x + 6$ $f (x) = - x + 6$
78. $f (x) = 4 + x$ $f (x) = 4 + x$
79. $f (x) = 20 - x$ $f (x) = 20 - x$
80. $f (x) = - 3 x + 13$ $f (x) = - 3 x + 13$
81. $f (x) = \frac{2}{5} x - 10$ $f (x) = \frac{2}{5} x - 10$
82. $f (x) = 3 x - 9$ $f (x) = 3 x - 9$
83. $f (x) = - x + 15$ $f (x) = - x + 15$
84. $f (x) = 4 - x$ $f (x) = 4 - x$

In each of Exercises 85–90, use the given graph to find each of the following: (a) the x-intercept and (b) the zero of the function.

Skill Maintenance

91. Write a slope–intercept equation for the line containing the point (−1, 4) and parallel to the line $3 x + 4 y = 7$ $3 x + 4 y = 7$ . [1.4]
92. Write an equation of the line containing the points (−5, 4) and (3, −2). [1.4]
93. Find the distance between (2, 2) and (−3, −10). [1.1]
94. Find the midpoint of the segment with endpoints $(- \frac{1}{2}, \frac{2}{5})$ $(- \frac{1}{2}, \frac{2}{5})$ and $(- \frac{3}{2}, \frac{3}{5})$ $(- \frac{3}{2}, \frac{3}{5})$ . [1.1]
95. Given that $f (x) = \frac{x}{x - 3}$ $f (x) = \frac{x}{x - 3}$ , find $f (- 3), f (0)$ $f (- 3), f (0)$ , and $f (3)$ $f (3)$ . [1.2]
96. Find the slope and the y-intercept of the line with the equation $7 x - y = \frac{1}{2}$ $7 x - y = \frac{1}{2}$ . [1.3]

Synthesis

State whether each of the following is a linear function.

97. $f (x) = 7 - \frac{3}{2} x$ $f (x) = 7 - \frac{3}{2} x$
98. $f (x) = \frac{3}{2 x} + 5$ $f (x) = \frac{3}{2 x} + 5$
99. $f (x) = x^{2} + 1$ $f (x) = x^{2} + 1$
100. $f (x) = \frac{3}{4} x - {(2.4)}^{2}$ $f (x) = \frac{3}{4} x - {(2.4)}^{2}$

Solve.

101. $2 x - {x - [3 x - (6 x + 5)]} = 4 x - 1$ $2 x - {x - [3 x - (6 x + 5)]} = 4 x - 1$
102. $14 - 2 [3 + 5 (x - 1)] =$ $14 - 2 [3 + 5 (x - 1)] =$ $3 {x - 4 [1 + 6 (2 - x)]}$ $3 {x - 4 [1 + 6 (2 - x)]}$
103. Packaging and Price. Dannon recently replaced its 8-oz cup of yogurt with a 6-oz cup and reduced the suggested retail price from 89 cents to 71 cents (Source: IRI). Was the price per ounce reduced by the same percent as the size of the cup? If not, find the price difference per ounce in terms of a percent.
104. Bestsellers. One week 10 copies of the novel The Last Song by Nicholas Sparks were sold for every 7.9 copies of David Baldacci’s Deliver Us from Evil that were sold (Source: USA Today Best-Selling Books). If a total of 10,919 copies of the two books were sold, how many copies of each were sold?
105. Running vs. Walking. A 150-lb person who runs at 6 mph for 1 hr burns about 720 calories. The same person, walking at 4 mph for 90 min, burns about 480 calories. (Source: FitSmart, USA Weekend, July 19–21, 2002) Suppose a 150-lb person runs at 6 mph for 75 min. How far must the person walk at 4 mph in order to burn the same number of calories burned running?

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Table of Contents for 1.5 Exercise Set

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Table of Contents for
1.5 Exercise Set