Beginning And Intermediate Algebra Student Solutions Manual
Beginning and Intermediate AlgebraStudent Solutions ManualComplete worked solutions to odd problemsSolutions manual has not been cross checked for accuracy.If you disagree with this solutions manual you should check with your instructor.Should you find an error, please E-mail tylerw@bigbend.edu so it can be corrected.Thank you!Beginning Algebra Student Solutions Manual by Tyler Wallace is licensed under aCreative Commons Attribution 3.0 Unported License. Permissions beyond the scope ofthis license may be available at http://wallace.ccfaculty.org/book/book.html.1
Beginning and Intermediate AlgebraStudent Solutions Manual Table of ContentsChapter 0: Arithmetic . 3Chapter 1: Solving Linear Equations . 11Chapter 2: Graphing Linear Equations . 40Chapter 3: Inequalities . 55Chapter 4: Systems of Equations . 62Chapter 5: Polynomials . 88Chapter 6: Factoring . 99Chapter 7: Rational Expressions . 109Chapter 8: Radical Expressions . 130Chapter 9: Quadratics . 144Chapter 10: Functions . 1892
Chapter 0: Arithmetic3
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Chapter 1: Solving Linear Equations11
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41) 25 555 2 43) 3 2 53 547) 223 4 2 34 2,222 5422055229333224 24 224226 , 6349)45) 104 1010 104 104466107676 ,464764,6 ,1041012945,1) c varies directly as a3) w varies inversely as x5) f varies jointly as x and y7) h is directly proportional to b9) a is inversely proportional to b2161212491361010108,1.71291291210
11) p is jointly proportional to q and r and p 12 when q 8 and r 313) t varies directly as the square of u and t 6 when u 315) w is inversely proportional to the cube of x and w is 54 when x 354 354 27145817) a is jointly proportional with the square of x and the square root of y anda 25 when x 5 and y 9 ·19) The electrical current, in amperes, in a circuit varies directly as the voltage. When 15 volts areapplied, the current is 5 amperes. What is the current when 18 volts are applied?1818621) Hooke’s law states that the distance that a spring is stretched by hanging object varies directly asthe mass of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance whenthe mass is 5 kg?33.322.
23) The number of aluminum cans used each year varies directly as the number of people using thecans. If 250 people use 60,000 cans in one year, how many cans are used each year in Dallas,which has a population of 1,008,000?2501,000,000,240 1,000,000,241,920,00025) According to Fidelity Investment Vision Magazine, the average weekly allowance of children variesdirectly as their grade level. In a recent year, the average allowance of a 9th-grade student was9.66 dollars per week. What was the average weekly allowance of a 4th-grade student?.1.0741.07 4 4.2827) The number of kilograms of water in a human body varies directly as the mass of the body. A 96kg person contains 64 kg of water. How many kilo grams of water are in a 60-kg person?60604029) The weight of an object on Mars varies directly as its weight on Earth. A person weighs 95lb onEarth weighs 38 lb on Mars. How much would a 100-lb person weigh on Mars?1001004031) The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty atank in 45 min at the rate of 600 kL/min, how long will it take the pump to empty the same tank atthe rate of 1000 kL/min?45 600270002723
33) The stopping distance of a car after the brakes have been applied varies directly as the square ofthe speed r. If a car, traveling 60 mph can stop in 200 ft, how fast can a car go and still stop in 72ft?1818 72 129636 35) The intensity of a light from a light bulb varies inversely as the square of the distance from the(watts per square meter) when the distance is 5 m. How muchbulb. Suppose intensity is 90 W/further would it be to a point where the intensity is 40 W/ ?90 590 252250 7.55 56.257.52.537) The intensity of a television signal varies inversely as the square of the distance from thetransmitter. If the intensity is 25 W/at a distance of 2 km, how far from the transmitter areyou when the intensity is 2.56 W/ ?25 225 4100. . 39.06256.251.81) When five is added to three more than a certain number, the result is 19. What is the number?3 5 198 19881124
3) When 18 is subtracted from six times a certain number, the result is 42. What is the number?61842181845) A number plus itself, plus twice itself, plus 4 times itself, is equal to 104. What is the number?24104137) Eleven less than seven times a number is five more than six times the number. Find the number.711 656611 511 11169) The sum of three consecutive integers is 108. What are the integers?::1:233 108333535, 36, 3711) Find three consecutive integers such that the sum of the first, twice the second, and three timesthe third is 76.:2 :21223 :3236687688142514, 13, 12
13) The sum of three consecutive odd integers is 189. What are the integers?::2:436 189666161, 63, 6515) Find three consecutive odd integers such that the sum of the first, two times the second, andthree times the third is 70.:2 :22243 :34312616 70161699, 11, 1317) Two angles of a triangle are the same size. The third angle is 12 degrees smaller than the firstangle. Find the measure the angles.:64:64:1264 12 52312 18012126464 , 64 , 52 19) The third angle of a triangle is the same size as the first. The second angle is 4 times the third. Findthe measure of the angles.:30:44 · 30 120:30302630 , 120 , 30
21) The second angle of a triangle is twice as large as the first. The measure of the third angle is 20degrees greater than the first. How large are the angles?:40:22 · 40 80:2040 20 60420 18020204040 , 80 , 60 23) The second angle of a triangle is five times as large as the first. The measure of the third angle is12 degrees greater than that of the first angle. How large are the angles?:24:55 · 24 120:1224 12 36712 18012122424 , 120 , 36 25) The second angle of a triangle is four times the first and the third is 5 degrees more than twice thefirst. Find the measures of the angles.:25:44 · 25 100:252 · 25 4 50 5 5575 180552525 , 100 , 55 27) The perimeter of a rectangle is 304 cm. The length is 40 cm longer than the width. Find the lengthand width.:4056 40 96:562 240304480 304808056275696
29) The perimeter of a rectangle is 280 meters. The width is 26 meters less than the length. Find thelength and width.:83:2683 26 572 226280452 280525283578331) A mountain cabin on 1 acre of land costs S30,000. If the land cost 4 times as much as the cabin,what was the cost of each?:6000:44 · 6000 240006000: 6,000,: 24,00033) A bicycle and a bicycle helmet cost S240. How much did each cost, if the bicycle cost 5 times asmuch as the helmet?:55 · 40 200:4040: 200,: 4035) If Mr. Brown and his son together had S220, and Mr. Brown had 10 times as much as his son, howmuch money had each?: 1010 · 20 200:2020.: 200,: 2037) Aaron had 7 times as many sheep as Beth, and both together had 608. How many sheep hadeach?:77 · 76 532:767628: 532,: 76
39) Jamal and Moshe began a business with a capital of S7500. If Jamal furnished half as much capitalas Moshe, how much did each furnish?:2500:22 · 2500 50002500: 2500,: 500041) A 6 ft board is cut into two pieces, one twice as long as the other. How long are the pieces?:22·2 4:224& 243) An electrician cuts a 30 ft piece of wire into two pieces. One piece is 2 ft longer than the other.How long are the pieces?:214 2 16:1422 30221416& 1445) The cost of a private pilot course is 1,275. The flight portion costs 625 more than the groundschool portion. What is the cost of each?:625325 625 950:3252625 1275625625325: 950,: 3251.91) rA boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find thepresent age of each.2Now 4H-boyx 10 x 141424Bxx 414 28Brother14862988: 16,:6
3) Pat is 20 years older than his son James. In two years Pat will be twice as old as James. How oldare they now?2Now 2Px 20 x 2222 22Jxx 222 242241844: 38,: 185) Fred is 4 years older than Barney. Five years ago the sum of their ages was 48. How old are theynow?48Now5Fx 4x-11548Bxx-526 486627: 31,: 277) Tim is 5 years older than JoAnn. Six years from now the sum of their ages will be 79. How old arethey now?79Now 6Tx 5 x 1111679Jxx 6217 79171731: 36,: 319) The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary. Findthe present age of each.2Now-4Jxx-442 28M32-x 28-x4 56 22234 56442030: 20,: 12
11) The sum of the ages of a china plate and a glass plate is 16 years. Four years ago the china platewas three times the age of the glass plate. Find the present age of each plate.3Now-4Cxx-443 12G16-x 12-x4 36 33344 364410: 10,:613) A is now 34 years old, and B is 4 years old. In how many years will A be twice as old as B?2Now tA3434 t342 4B44 t348 2348268815) An Oriental rug is 52 years old and a Persian rug is 16 years old. How many years ago was theOriental rug four times as old as the Persian Rug?4Now-tO5252-t524 16P1616-t5264 44452 3645252417) The age of the older of two boys is twice that of the younger; 5 years ago it was three times thatof the younger. Find the age of each.3Now-5O2x2x-525 35Yxx-525 31522515151510: 20,: 1031
19) Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are theynow?13Now-7M2x2x-727713Cxx-7314 1314149: 18,:921) A silver coin is 28 years older than a bronze coin. In 6 years, the silver coin will be twice as old asthe bronze coin. Find the present age of each coin.2Now 6Sx 28 x 343426Bxx 634 2123412221212: 50,: 2223) A limestone statue is 56 years older than a marble statue. In 12 years, the limestone will be threetimes as old as the marble statue. Find the present age of the statues.3Now 12Lx 56 x 6868312Mxx 1268 33668362363616: 72,: 1625) Brandon is 9 years older than Ronda. In four years the sum of their ages will be 91. How old arethey now?91Now 4Bx 9 x 1313491Rxx 4217 9117 173732: 46,: 37
27) A father is three times as old as his son, and his daughter is 3 years younger than the son. If thesum of their ages 3 years ago was 63 years, find the present age of the father.63Now-3F3x3x-3333663Sxx-3512 63Dx-3x-6121215: 45,15,: 1229) The sum of the ages of two ships is 12 years. Two years ago, the age of the older ship was threetimes the age of the newer ship. Find the present age of each ship.3Now-2Oxx-223 10Y12-x 10-x2 3022230288 & 431) Ann is eighteen years older than her son. One year ago, she was three times as old as her son.How old are they now?3Now-1Ax 18 x 171731Sxx-117 331731033233: 28,: 10
33) A mosaic is 74 years older than the engraving. Thirty years ago, the mosaic was three times as oldas the engraving. Find the present age of each.3Now -30Mx 74 x 4444330Exx-3044 39044902909067: 141,: 6735) A wool tapestry is 32 years older than a linen tapestry. Twenty years ago, the wool tapestry wastwice as old as the linen tapestry. Find the present age of each.2Now -20Wx 32 x 1212220Lxx-2012 2201220322020: 84,: 5237) Nicole is 26 years old. Emma is 2 years old. In how many years will Nicole be triple Emma’s age?3Now tN2626 t263 2E22 t266 32666621039) Mike is 4 years older than Ron. In two years, the sum of their ages will be 84. How old are theynow?84Now 2Mx 4x 66284Rxx 228 84883834: 42,: 38
1.101) A is 60 miles from B. An automobile at A starts for B at the rate of 20 miles an hour at the sametime that an automobile at B starts for A at the rate of 25 miles an hour. How long will it be beforethe automobiles meet?202560rtdA 20 t 20tB 25 t 25t1.333) Two trains travel toward each other from points which are 195 miles apart. They travel at rate of25 and 40 miles an hour respectively. If they start at the same time, how soon will they meet?2540195rtd25 t 25t40 t 40t35) A passenger and a freight train start toward each other at the same time from two points 300miles apart. If the rate of the passenger train exceeds the rate of the freight train by 15 miles perhour, and they meet after 4 hours, what must the rate of each be?4460 300rtdP r 15 4 4r 60860 300Fr44r606030: 45,: 307) A man having ten hours at his disposal made an excursion, riding out at the rate of 10 miles anhour and returning on foot, at the rate of 3 miles an hour. Find the distance he rode.1030 3rtDr 10t10t33w 3 10-t 30-3t109) A boy rides away from home in an automobile at the rate of 28 miles an hour and walks back atthe rate of 4 miles an hour. The round trip requires 2 hours. How far does he ride?288 4rtdr 28t28t44w 4 2-t 8-4t.2528 . 25357.
11) A family drove to a resort at an average speed of 30 mph and later returned over the same road atan average speed of 50 mph. Find the distance to the resort if the total driving time was 8 hours.30400 50rtdT 30t30t5050R 50 8-t 400-50t530 5150.13) A, who travels 4 miles an hour starts from a certain place 2 hours in advance of B, who travels 5miles an hour in the same direction. How many hours must B travel to overtake A?48 5rtDA4 t 2 4t 844B5t5t815) A motorboat leaves a harbor and travels at an average speed of 8 mph toward a small island. Twohours later a cabin cruiser leaves the same harbor and travels at an average speed of 16 mphtoward the same island. In how many hours after the cabin cruiser leaves will the cabin cruiser bealongside the motorboat?816 16rtdM 8 t 2 8t 1688C 16t16t217) A car traveling at 48 mph overtakes a cyclist who, riding at 12 mph, has had a 3 hour head start.How far from the starting point does the car overtake the cyclist?481236rtdCar 48t48t1212Cy 12 t 3 12t 36148 148.19) Two men are traveling in opposite directions at the rate of 20 and 30 miles an hour at the sametime and from the same place. In how many hours will they be 300 miles apart?2030300rtd20 t 20t30 t 30t630036
21) A motorboat leaves a harbor and travels at an average speed of 18 mph to an island. The averagespeed on the return trip was 12 mph. How far was the island from the harbor if the total trip took5 h?1860 12rtdT 18t18t1212R 12 5-t 60-12t218 23623) A jet plane traveling at 570 mph overtakes a propeller-driven plane that has had a 2 h head start.The propeller-driven plane is traveling at 190 mph. How far from the starting point does the jetovertake the propeller-driven plane?570190380rtdJ 570 t570t190190P 190 t 2 190t 3801570 1570.25) As part of flight training, a student pilot was required to fly to an airport and then return. Theaverage speed on the way to the airport was 100 mph, and the average speed returning was 150mph. Find the distance between the two airports if the total flight time was 5 h.100750 150rtdT 100t100t150150R 150 5-t 750-150t3100 3300.27) A car traveling at 56 mph overtakes a cyclist who, riding at 14 mph, has had a 3 h head start. Howfar from the starting point does the car overtake the cyclist?561442rtdCar 56t56t1414Cy 14 t 3 14t 42156 13756
29) A bus traveling at a rate of 60 mph overtakes a car traveling at a rate of 45 mph. If the car had a 1h head start, how far from the starting point does the bus overtake the car?604545rtdB 60t60t4545C 45 t 1 45t 45360 3180.31) A truck leaves a depot at 11 A.M. and travels at a speed of 45 mph. At noon, a van leaves thesame place and travels the same route at a speed of 65 mph. At what time does the van overtakethe truck?4545 65rtdT 45 t 1 45t 454545V 65t65t2.252.25 212: 0015.2: 15 2: 1533) Three campers left their campsite by canoe and paddled downstream at an average rate of 10mph. They then turned around and paddled back upstream at an average rate of 5 mph to returnto their campsite. How long did it take the campers to canoe downstream if the total trip took 1hr?105 5rtdd 10t10t55v5 1-t 5-5t20.35) A student walks and jogs to college each day. The student averages 5 km/hr walking and 9 km/hrjogging. The distance from home to college is 8 km, and the student makes the trip in one hour.How far does the student jog?59 98rtdW 5t5t49 8J9 1-t 9-9t998938.259 . 2592.256.75
37) On a 220 mi trip, a car traveled at an average speed of 50 mph and then reduced its averagespeed to 35 mph for the remainder of the trip. The trip took a total of 5 h. How long did the cartravel at each
Solutions manual has not been cross checked for accuracy. If you disagree with this solutions manual you should check with your instructor. Should you find an error, please E-mail tylerw@bigbend.edu so it can be corrected. Thank you! Beginning Algebra Student Solutions Manual by Tyler Wallace is licensed under a
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