# 100 Hard Word Problems in Algebra (2023)

Find below a wide variety of hard word problems in algebra. Most tricky and tough algebra word problems are covered here. If you can solve these, you can probably solve any algebra problems.Teachers! Feel free to select from this list and give them to your students to see if they have mastered how to solve tough algebra problems.Find out below how you can print these problems. You can also purchase a solution if needed.

1.Thecost of petrol rises by 2 cents a liter. last week a man bought 20liters at the old price. This week he bought 10 liters at the newprice. Altogether, the petrol costs \$9.20. What was the old price for1 liter?

2.Teachersdivided students into groups of 3. Each group of 3 wrote a reportthat had 9 pictures in it. The students used 585 pictures altogether.How many students were there in all?

3. Veraand Vikki are sisters. Vera is 4 years old and Vikki is 13 years old.What age will each sister be when Vikki is twice as old as Vera?

4.Acan do a work in 14 days and working together A and B can do the samework in 10 days. In what time can B alone do the work?

5. 7workers can make 210 pairs of cup in 6 days. How many workers arerequiredto make 450 pairs of cup in 10 days?

6. Tenyears ago the ratio between the ages of Mohan and Suman was 3:5.11years hence it will be 11:16. What is the present age of Mohan?

7. Theratio of girls to boys in class is 9 to 7 and there are 80 studentsinthe class. How many girls are in the class?

8. Oneounce of solution X contains only ingredients a and b in a ratio of2:3.One ounce of solution Y contains only ingredients a and b in a ratioof1:2. If solution Z is created by mixing solutions X and Y in a ratioof3:11, then 2520ounces of solution Z contains how many ounces of a?

9. Thisweek Bob puts gas in his truckwhen the tank was about halfempty.Five days later, bob puts gas again when the tank was aboutthreefourths full. If Bob Bought 24 gallons of gas, how many gallonsdoesthe tank hold?

10. Acommercialairplane flying with a speed of 700 mi/h is detected 1000milesaway with a radar. Half an hour later an interceptor plane flyingwitha speed of 800 mi/h is dispatched. How long will it take theinterceptorplane to meet with the other plane?

11. Thereare 40 pigs and chickens in a farmyard. Joseph counted 100 legsinall. How many pigs and how many chickens are there?

12. Thetop of a box is a rectangle with a perimeter of 72 inches. If theboxis 8 inches high, what dimensions will give the maximum volume?

13. Youare raising money for a charity. Someone made a fixed donationof500. Then, you require each participant to make a pledge of25dollars. What is the minimum amount of money raised if there are 224participants.

14. Thesum of two positive numbers is 4 and the sum of their squaresis28.What are the two numbers?

15. Flyingagainst the jet stream, a jet travels 1880 mi in 4 hours. Flyingwiththe jet stream, the same jet travels 5820 mi in 6 hours. What istherate of the jet in still air and what is the rate of the jetstream?

16.Jennaand her friend, Khalil, are having a contest to see who can savethemost money. Jenna has already saved \$110 and every week she savesanadditional \$20. Khalil has already saved \$80 and every week he savesanadditional \$25. Let x represent the number of weeks and y representthetotal amount of money saved. Determine in how many weeks Jenna andKhalilwill have the same amount of money.

17. Thesum of three consecutive terms of a geometric sequence is 104 andtheirproduct is 13824.find the terms.

18. Thesum of the first and last of four consecutive odd integers is 52.Whatare the four integers?

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19. Ahealth club charges a one-time initiation fee anda monthly fee. Johnpaid100 dollars for 2 months of membership. However, Peter paid 200 for6months of membership. How much will Sylvia pay for 1 year ofmembership?

20. Thesum of two positive numbers is 4 and the sum of their cubes is 28.Whatis the product of the two numbers?

21. Aman selling computer parts realizes that when he sells 16 computerparts,his earning is \$1700. When he sells 56 computer parts, hisearningis \$4300. What will the earning be if the man sells 30 computersparts?

22. Aman has 15 coins in his pockets. These coins are dimes and quartersthataddup 2.4 dollars. How many quarters and how many dimes does the manhave?

23. Thelengths of the sides of a triangle are in the ratio 4:3:5. Findthelengthsof the sides if the perimeter is 18 inches.

24. Theratio of base to height of a equilateraltriangle is 3:4. If the areaofthe triangle is 6, what is the perimeter of the triangle?

25. Thepercent return rate of a growth fund, income fund, and money marketare10%, 7%, and 5% respectively. Suppose you have 3200 to invest and youwantto put twice as much in the growth fund as in the money market tomaximizeyour return. How should you invest to get a return of 250dollarsin 1 year?

26. Ashark was caught whose tail weighted 200 pounds. The head of thesharkweightedas much as its tail plus half its body. Its body weighted asmuchas its head and tail. What is the weight of the shark?

27. Thesquare root of anumber plus two is the same as thenumber. Whatisthenumber?

28. Supposeyou have a coupon worth 6 dollars off any item at a mall. You gotoa store at the mall that offers a 20% discount. What do you need todotosave the most money?

29. Supposeyour grades on three math exams are 80, 93, and 91. What grade doyouneed on your next exam to have at least a 90 average on the fourexams?

30. Peterhas a photograph that is 5 inches wide and 6 inches long. Sheenlargedeach side by the same amount. By how much was the photographenlargedif the new area is 182 square inches?

31. Thecost to produce a book is 1200 to get started plus 9dollars per book. Thebook sells for 15 dollars each. How many books must be sold to make aprofit?

32. StoreA sells CDsfor 2 dollars each if you pay a one-timefee of104dollars. Store B offers 12 free CDs and charges 10 dollars for eachadditionalCD. How many CD must you buy so it will cost the same underbothplans?

33. When4 is added to two numbers, the ratio is 5:6. When 4 is subtractedfrom the two numbers, the ratio is 1:2. Find the two numbers.

34. Astore owner wants to sell 200 pounds of pistachios and walnuts mixedtogether. Walnuts cost 4 dollars per pound and pistachio cost 6dollarsperpounds. How many pounds of each type of nuts should be mixed if thestore owner will charge 5 dollars for the mixture?

35. Acereal box manufacturer makes 32-ounce boxes of cereal. In a perfectworld, the box will be 32-ounce every time is made. However, since theworld is not perfect, they allow a difference of 0.06 ounce. Find therange of acceptable size for the cereal box.

36. Aman weighing 600 kg has been losing 3.12% of his weight each monthwithsomeheavy exercises and eating the right food. What will the man weighafter20 months?

37. Anobject is thrown into the air at a height of 60 feet. After 1 secondand2 second, the object is 88 feet and 84 feet in the air respectively.Whatis the initial speed of the object?

38. Atransit is 200 feet from the base of a building. There is manstanding on top of the building. The angles of elevation from the topand bottom of the man are 45 degrees and 44 degrees. What is theheight of the man?

39. Alemonade consists of 6% of lemon juice and a strawberry juiceconsists of 15% pure fruit juice. How much of each kind should bemixed together to get a 4 Liters of a 10% concentration of fruitjuice?

40. Ellencan wash her car in 60 minutes. Her older sister Sarah can do thesame job in 45 minutes. How long will it take if they wash the cartogether?

41. Aplane flies 500 mi/h. The plane can travel 1100 miles with the windin the same amount of time as it travels 900 miles against the wind.What is the speed of the wind?

42. Acompany produces boxes that are 5 feet long, 4 feet wide, and 3 feethigh. The company wants to increase each dimension by the same amountso that the new volume is twice as big. How much is the increase indimension?

43. Jamesinvested half of his money in land, a tenth in stock, and a twentiethin saving bonds. Then, he put the remaining 21000 in a CD. How muchmoney did James saved or invested?

44. Themotherboards for a desktop computer can be manufactured for 50dollarseach.The development cost is 250000. The first 20 motherboard are samplesandwill not be sold. How many salable motherboards will yield an averagecostof 6325 dollars?

45. Howmuch of a 70% orange juice drink must be mixed with 44 gallons of a20% orange juice drink to obtain a mixture that is 50% orange juice?

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46. Acompany sells nuts in bulk quantities. When bought in bulk, peanutssellfor \$1.20 per pound, almonds for \$ 2.20 per pound, and cashewsfor \$3.20 per pound. Suppose a specialty shop wants a mixture of 280pounds that will cost \$2.59 per pound. Find the number of pounds ofeach type of nut if the sum of the number of pounds of almonds andcashews is three times the number of pounds of peanuts. Round youranswers to the nearest pound.

47. ABasketball player has successfully made 36 of his last 48 freethrows.Findthe number of consecutive free throws the player needs to increasehissuccess rate to 80%.

48. Johncan wash cars 3 times as fast as his son Erick. Working together,they need to wash 30 cars in 6 hours. How many hours will it takeseach of them working alone?

49. Ina college, about 36% of student are under 20 years old and 15% areover 40 years old. What is the probability that a student chosen atrandom is under 20 years old or over 40 years?

50. Twicea number plus the square root of the number is twelve minus thesquare root of the number.

51. Thelight intensity, I , of a light bulb varies inversely as the squareofthedistance from the bulb. A a distance of 3 meters from the bulb, I =1.5 W/m^2 .What is the light intensity at a distance of 2 meters from thebulb?

52. Thelengths of two sides of a triangle are 2 and 6. find the range ofvalues for the possible lengths of the third side.

53. Findthree consecutive integers such that one half of their sum is between15 and 21.

54. Afteryou open a book, you notice that theproduct of thetwo page numbersonthe facing pages is 650. What are the two page numbers?

55. Supposeyou start with a number. You multiply the number by 3, add 7, divideby Â½, subtract 5, and then divide by 12. The result is 5. Whatnumber did you start with?

56. Youhave 156 feet of fencing to enclose a rectangular garden. You wantthe garden to be 5 times as long as it is wide. Find the dimensionsof the garden.

57. Theamount of water a dripping faucet wastes water varies directly withthe amount of time the faucet drips. If the faucet drips 2 cups ofwater every 6 minutes, find out how long it will take the faucet todrip 10.6465 liters of water.

58. Awasher costs 25% more than a dryer. If the store clerk gave a 10%discountfor the dryer and a 20% discount for the washer, how much isthewasher before the discount if you paid 1900 dollars.

59. Bakinga tray of blueberry muffins takes 4 cups of milk and 3 cups of wheatflour. A tray of pumpkin muffins takes 2 cups of milk and 3 cups ofwheat flour. A baker has 16 cups of milk and 15 cups of wheat flour.You make 3 dollars profit per tray of blueberry muffins and 2 dollarsprofit per tray of pumpkin muffins. How many trays of each type ofmuffins should you make to maximize profit?

60. Acompany found that -2p + 1000 models the number of TVs sold per monthwhere p can be set as low as 200 or as high as 300. How can thecompany maximize the revenue?

## More hard word problems in algebra

61. Yourfriends say that he has \$2.40 in equal numbers of quarters, dimes,and nickels. How many of each coin does he have?

62. Iam a two-digit number whose digit in the tenth place is 1 less thantwice the digit in the ones place. When the digit in the tenth placeis divided by the digit in the ones place, The quotient is 1 and theremainder is 4. What number am I?

63. Atwo-digit number is formed by randomly selecting from the digits 2,4,5,and 7 without replacement. What is the probability that a two-digitnumbercontains a 2 or a 7?

64. Supposeyou interview 30 females and 20 males at your school to find out whoamong them are using an electric toothbrush. Your survey revealedthat only 2 males use an electric toothbrush while 6 females use it.What is the probability that a respondent did not use an electrictoothbrush given that the respondent is a female?

65. Anemployer pays 15 dollars per hour plus an extra 5 dollars per hourfor every hour worked beyond 8 hours up to a maximum daily wage of220 dollars. Finda piecewise function that models this situation.

66. Divideme by 7, the remainder is 5. Divide me by 3, the remainder is 1 andmy quotient is 2 less than 3 times my previous quotient. What numberam I?

67. Acompany making luggagehave these requirements to follow. The lengthis15 inches greater than the depth and the sum of length, width, anddepth may not exceed 50 inches. What is the maximum value for thedepth if the manufacturer will only use whole numbers?

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68. Tomake an open box, a man cuts equal squares from each corner of asheet of metal that is 12 inches wide and 16 inches long. Find anexpression for the volume in terms of x.

69. Tencandidates are running for president, vice-president, and secretaryin the students government. You may vote for as many as 3 candidates.In how many ways can you vote for 3 or fewer candidates?

70. Thehalf-life of a medication prescribed by a doctor is 6 hours.Howmany mg of this medication is left after 78 hours if the doctorprescribed100 mg?

71. Supposeyou roll a red number cube and a yellow number cube.FindP(red 2, yellow 2) and the probability to get any matching pairs ofnumbers.

72. Amovie theater in a small town usually open its doors 3 days in a rowand then closes the next day for maintenance. Another movie theater 3miles away open 4 days in a row and then closes the next day for thesame reason. Suppose both movie theaters are closed today and todayis Wednesday, when is the next time they will both be closed again onthe same day?

73. Aninvestor invests 5000 dollars at 10% and the rest at 5%. How much wasinvested at 5% if the yield is one-fifth of the amount invested at at10%?

74. 20000students took a standardized math test. The scores on the test arenormally distributed, with a mean score of 85 and a standarddeviation of 5. About how many students scored between 90 and 95?

75. Asatellite, located 2400 km above Earthâ€™s surface, is in circularorbit around the earth. If it takes the satellite 3 hours to complete1 orbit, how far is the satellite after 1 hour?

76. Ina group of 10 people, what is the probability that at least twopeopleinthe group have the same birthday?

77. Duringa fundraising for cancer at a gala, everybody shakes hands witheveryone else in the room before the event and after the event isfinished.Ifn people attended the gala, how many different handshakes occur?

78. Twocubes have side lengths that are equal to 2x and 4x. How many timesgreaterthan the surface of the small cube is the surface area of thelargecube?

79. Supposeyou have a job in a restaurant that pays \$8 per hour. You also havea job at Walmart that pays \$10 per hour. You want to earn at least200 per week. However, you want to work no more than 25 hours perweek . Show 3 different ways you could work at each job.

80. Twocompany offer tutoring services. Company A realizes that when theytutor for 3 hours, they make 45 dollars. When they tutor for 7 hoursthey make 105 hours. Company B realizes that when they tutor for 2hours, they make 34 dollars. When they tutor for 6 hours they make102 hours. Assuming that the number of hours students sign fortutoring is the same for both company, which company will generatemore revenue?

81. Youwant to fence a rectangular area for kids in the backyard. To save onfences, you will use the back of your house as one of the four sides.Find the possible dimensions if the house is 60 feet wide and youwant to use at least 160 feet of fencing.

82. Whena number in increased by 20%, the result is the same when it isdecreased by 10% plus 12. What is the number?

83. Theaverage of three numbers is 47. The biggest number is five more thantwice the smallest. The range is 35. What are the three numbers?

84. Thepercent of increase of a number from its original amount to 36 is80%.Whatis the original amount of the number?

85. WhenPeter drives to work, he averages 45 miles per hour because oftraffic. On the way back home, he averages 60 miles per hour becausetraffic is not as bad. The total travel time is 2 hours. How far isPeterâ€™s house from work?

86. Anadvertising company takes 20% from all revenue that it generates forits affiliates. If the affiliates were paid 15200 dollars this month,how muchrevenuedid the advertising company generate this month?

87. Acompanyâ€™s revenue can be modeled with a quadratic equation. Thecompany noticed that when they sell either 2 or or 12 items, therevenue is 0. How much is the revenue when they sell 20 items?

88. Aball bounced 4 times, reaching three-fourths of its previous heightwith each bounce. After the fourth bounce, the ball reached a heightof 25 cm. How high was the ball when it was dropped?

89. Arental company charges 40 dollars per day plus \$0.30 per mile. Yourent a car and drop it off 4 days later. How many miles did you drivethe car if you paid 325.5 dollars which included a 5% sales tax?

90. Twostudents leave school at the same time and travel in oppositedirections along the same road. One walk at a rate of 3 mi/h. Theother bikes at a rate of 8.5 mi/h. After how long will they be 23miles part?

91. Brownhas the same number of brothers as sisters. His sister Sylvia astwice as many brothers as sisters. How many children are in thefamily?

92. Ethanhas the same number of male classmates as female classmates. Hisclassmate Olivia has three-fourths as many female classmates as maleclassmates. How many students are in the class?

93. Noahwants to share a certain amount of money with 10 people. However, atthe last minute, he is thinking about decreasing the amount by 20 sohe can keep 20 for himself and share the money with only 5 people.How much money is Noah trying to share if each person still gets thesame amount?

94. Thesquare root of me plus the square root of me is me. Who am I?

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95. Acash drawer contains 160 bills, all 10s and 50s. If the total valueof the 10s and 50s is \$1,760. How many of each type of bill are inthe drawer?

96. Youwant to make 28 grams of protein snack mix made with peanuts andgranola. Peanuts contain 7 grams of protein per ounce and granolacontain 3 grams of protein per ounce. How many ounces of granolashould you use for 1 ounce of peanuts?

97. Thelength of a rectangular prism is quadrupled, the width is doubled,and the height is cut in half. If V is the volume of the rectangularprism before the modification, express the volume after themodification in terms of V.

98. Acar rental has CD players in 85% of its cars. The CD players arerandomly distributed throughout the fleet of cars. If a person rents4 cars, what is the probability that at least 3 of them will have CDplayers?

99. Jacobâ€™shourly wage is 4 times as much as Noah. When Jacob got a raise of 2dollars, Noah accepted a new position that pays him 2 dollars lessper hour. Jacob now earns 5 times as much money as Noah. How muchmoney do they make per hour after Jacob got the raise?

100.

Youown a catering business that makes specialty cakes. Your company hasdecided to create three types of cakes. To create these cakes, ittakes a team that consists of a decorator, a baker, and a designconsultant. Cake A takes the decorator 9 hours, the baker 6 hours,and the design consultant 1 hour to complete. Cake B takes thedecorator 10 hours, the baker 4 hours, and the design consultant 2hours. Cake C takes the decorator 12 hours, the baker 4 hour, and thedesign consultant 1 hour. Without hiring additional employees, thereare 398 decorator hours available, 164 baker hours available, and 58design consultant hours available. How many of each type of cake canbe created?

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Hard word problems in algebra

Algebra word problems

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