Word+Problems

=Word Problems=
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NOTE* Sometimes, there are hints... and sometimes, things are added to confuse cheaters 1. Find three positive, even consecutive numbers that have a sum of 162. [psiriya] //Edited by [ajeyarajah]//

2. The difference between a number and its square is 6. Find the possible values of the number. [psiriya]

3. A manufacturer of TV sets wants us to analyze the effectiveness of an advertising campaign it has been running locally. The manufacturer reports that during a three-month period it spent $9500 and sold 16 500 sets. In the next three-month period, it spent $22 000 and sold 18 250 sets. The client believes there is a linear relationship between the amount spent and the number of TVs sold. She wants to know the linear equation relating the number of sets sold to the amount spent on advertising. She also wants to know what the estimated sales would be if the ad budget were raised to $30 000.

4. A manufacturing plant burns fossil fuel in its manufacturing process. The fuel that it obtains can be divided into three types: low-emission fuel, moderate-emission fuel, and high-emission fuel; federal law requires that high-emission fuel be returned for processing and allows that no more than 20% of the plant's fuel may be moderate-emission fuel. The company gets its fuel from two different sources: fuel from source 1 costs $6 per tonne and consists on average of 52% low-emission fuel, 28% moderate-emission fuel, and the rest high-emission fuel; fuel from source 2 costs $7 per tonne and consists on average of 60% low-emission fuel, 10% moderate-emission fuel, and the rest high-emission fuel. The company needs at least 290 tonnes of usable fuel each day. How much fuel should it buy from each source in order to minimize cost? What is this minimum cost?

5. Your teacher is giving you a test worth 100 points and containing 40 questions. There are 2-point and 4-point questions on the test. How many of each type of question are on the test?

6. Navitha is going on a road trip. She drives at 50 km/h. What distance will she have covered in each hour of the first five hours? Graph the relation. At this rate, how fast will she have driven after 6 1/2 hours? [FNanji]

7. Three even numbers have a mean of 50. If the largest number is 60, calculate the lowest possible value for the smallest number. [vdesai and bjia]

8. Bert is standing 33 m away from a building, looking up at its summit. If the distance from the top of Bert's head to the top of the building is 55 m, and if Bert is 180 cm tall, what is the height of the building? [vdesai and bjia]

9. The product of two positive integers is 57. The first integer is one-third the product. The second integer is 4 less than the first integer. Find the integers. [apaulraj]

10. In an isosceles triangle, one of the equal sides is 3 m less than twice its base. The perimeter of the triangle is 54 m. Find the length of the sides. [sjeyakanthakumar]

11. A tour bus left Toronto for Edmonton at 10:00 am and drove at 80 km/h. Half an hour later, another tour bus left Toronto for Edmonton and drove at 100 km/h. (a) How long did it take the second tour bus to overtake the first one? (b) At what time did this happen? [a_zhang, A-Liu, ATaheri-Dezfouli, Christina]

 12. A pole made of batons is 62 cm long. Chris has green batons, each 3 cm long, and yellow batons, each 5 cm long. How many combinations are there for him to make the pole IF THE TOTAL NUMBER OF BATONS IS 15? Hint: This is a linear relations question [Christina, a_zhang, Anthony, ATaheri-Dezfouli]

13. Arash, Anthony, Anne, and Christina are the founders of the recently successful computer company, Pear. They made a profit of $6.4 x 10⁸ and are going to share it in a ratio of 3 : 6 : 5 : 4 respectively. How much does each founder receive? [ATaheri-Dezfouli, Christina, a_zhang, A-Liu ]



14. A rectangular swimming pool with a length that is 50 cm shorter than twice the width is surrounded by tiles each half a metre wide. The pool perimeter is 16 m. What is the perimeter of the pool including the tiles surrounding it? [Christina, a_zhang, A-Liu, ATaheri-Dezfouli]

15. A vendor sells hot dogs, hamburgers, and sausages. A customer buys 4 hot dogs, 5 hamburgers, and 4 sausages for $30.66. The price of a hot dog is $1.00 more than the price of a hamburger. The price of a sausage is $2.00 less than the price of 2 hamburgers. Find the cost of each item. [kevink2435]

16. If Kevin earns $132 in 9 h, how much does he earn in 20 h? [kevink2435]

17. Kevin works in a shoe-selling store. He earns $1299/week, plus a commission of 20% of his sales. (a) Write the partial-variation equation to describe his earning in one week. (b) If Kevin earned $100 000 000 in one week, what is the total value of all the shoes he sold? [kevink2435]

18. The formula for volume is V=lwh. Is this equation a direct variation or a partial variation. Explain your reasoning. [kevink2435]

19. For the first 5 seconds, Kevin can run at a speed of 25 km/h. If his rate of speed drops continuously by 2 km/h every 5 seconds, then what's the total distance in kilometres that he ran before he came to a stop? [kevink2435]

20. Three dudes went to a beach on a Sunday afternoon. Dude #1 applied 32 mL of sunscreen. Dude #2, who was taller, applied more than twice the amount Dude #1 applied. Dude #3 used one third of the amount of sunscreen Dude #2 used. Altogether they used 120 mL of sunscreen. Identify the amount Dude #2 and Dude #3 applied. Round your answers to the nearest unit. [Apasricha and h_singh]

21. Two girls decided to donate their hair to cancer patients. Julie had the longest hair. Her friend Kim's hair was 3/4 the length of Julie's hair. Together the girls had 140 cm of hair. Unwilling to go bald they each decided to keep 5 cm of their hair. (a) Identify the length of Julie's hair and Kim's hair. (b) In the end what is the length of the hair that the girls decided to donate? [Apasricha and h_singh]

22. The length of a rectangle is 15 cm more than twice its width. The perimeter of the rectangle is 60 cm. Find the length and the width of the rectangle. [S.Swamy]

23. Sam earns $12/hr at a local restaurant. He works 3 hours a day. How long will it take Sam to earn $252? [S.Swamy]

24. The square of a number and the cube of the same number add up to 12. One half of the squared number is 3/2 more that one sixteenth of the cubed number. Find the two numbers. [psiriya and dpan]

25. Ambrose walks 15 miles per hour. It takes him 3 hours and 20 minutes to walk to school from his house. How far away is the school from his house? [C. Hung and Kavi]

26. Bob and Marley are standing side by side in a photograph. In the photo, Bob is 25 mm and Marley is 30 mm. If Bob is 185 cm tall in real life, how tall is Marley in real life? [C. Hung and Kavi]

27. Sasha took 5 hours to drive 470 km from North Bay to Stratford, Ontario. During part of the trip, she drove on the highway at 100 km/h, and for the remainder of the trip, she drove at 90 km/h. How far did she drive at 100 km/h and at 90 km/h? [slakkunarajah]

28. Alexis is 2 years younger than Maria. Six years ago, Maria was twice as old as Alexis. How old are they now? [lshui]

29. Alex can paint his room in 4 days. If his dad helps him, they can complete the job in 2 days. How long will it take his dad to paint the room alone? [lshui]

30. Ron and April are travelling from Toronto to Ottawa. Ron leaves at 8 a.m. and drives at 50 km/h. April leaves at 10 a.m and drives at 70 km/h. When will April overtake Ron? [lshui]

31. After nine exams, Henry's mean score was 75. Then, after a tenth exam, his mean score became 90. Each exam had a total of 100 marks and the last exam had 5 bonus questions. What mark did Henry get on his last exam? How many marks was each bonus question worth? [hli] Yes, this is extremely unrealistic...

32. How many cubes are there in a Professor's Cube ( 5 x 5 x 5 Rubik's Cube)? [ hli] Hint: There are obviously no cubes inside.

33. The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. [N_Anil],[n_nandakumar]

34. Fifteen balloons are arranged in a circle. The distance from the first balloon to the second is 9 cm; the distance from the second to the third is 12 cm, and the distance from the third to the fourth is 15 cm. At this rate, what is the circumference of the circle? [kevink2435]

35. Steven has a pocket full of change in  quarters and dimes only. He has a total of $5.40. a circle. The amount of dimes are twice as much as the quarters. How many dimes and quarters does Steven have? [m_sanghvi, l_leung and Yuanling]

36. Jonathan received  a mark of 75% on a test that was out of 35. Bala received an 80% on the same test. Disha got 20 out of 22 on a different test. How much, out of 35 did Bala and Jonathan get, and what  was the percentage that Disha received? [djani, bthevakumar, jgnanapragasam]

37. A car travels at the rate of 75 km/h for 35 minutes. A bus travels at 110 km/h for the same amount of time. How far did each travel in 25 minutes? [djani, bthevakumar, jgnanapragasm]

38. The Happy Face Cell Phone company charges $50 per month plus 15 cents per minute, while the Blue Star Cell Phone Company charges no monthly fee but 25 cents per minute. After how many minutes of using the phone would the monthly phone bill be the same from both companies? [N_Anil, N_Nandakumar]

39. There are 5 groups in a class, each group starts with the same amount of money summing up to £200, but adds more from their own pocket except for group 4. The total amount ends up as £500. Group 1 has double the amount of group 4; group 2 has £20 less than group 1; group 3 has 3 times the amount group 1 has and group 5 has a the same amount as group 1. How much money did each group start with? And how much did they add to it? [lbatilando]

40. Three friends won a contest that gave them $10 000 as a cash prize. Jerry was to receive $1000 more than Annie, and David was to receive $700 less than Jerry. How much money does each friend receive? [akunasegaram]

41. Simon is twice as old as David. Ten years ago Simon was four times as old as David. How old is David at present? [rkumarahuru]

42. Joseph is 15 years older than John at present. 7 years hence Joseph will be twice as old as John. How old is John at present. [rkumarahuru]

43. Every month, Jay gets allowance. Assume last year he had no money, and kept it up to now. Then he spends 1/2 of his money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After he bought all of that, he had $7777 left. Assuming he only gets money by allowance, how much money does he earn every month? [JRathod]

44. You have two blocks of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay? [JRathod]

45. A swimming pool is 20 m by 15 m. It is surrounded by a walkway. The outside perimeter of the walkway is 78 m. What is the width of the walkway? (sshanmuganantham)

46. Find a number which decreased by 18 is 5 times its opposite. (pvasdev)

47. Judith can type 300 words in 5 min. a) How many words can Judith type in 13 minutes? b) How long will it take for her to type 5,756 words? [rmardhani]---edited by [kevink2435]

48. The distance from Kevin's home to his school is 10 km. For the first 5 hours, Kevin ran at a constant speed of 14 m/h to school from his home. Then, his friend's mom spotted him and offered to drive him the rest of the way to school. If the car travelled at a constant speed of 100 m/h and he left for school at 3:00 A.M., then at what time would he finally arrive to school? [kevink2435]

49. Kevin's allowance varies directly as the square of his sister's allowance. If Kevin's allowance is $0.9 and his sister's is $0.5, find Kevin's allowance when his sister's is $22. [kevink2435]

50. Kevin always wanted to have a dog so he decided to buy one at a dollar store. After purchasing the dog, he only had $2000 left in his bank account. If maintaining a dog costs $22 per month, then for how many years can Kevin support his dog before he goes completely bankrupt? :) [kevink2435]

51. Bob works at Sportschek selling shoes for a living. Bob gets $30 an hour and 15% of all the shoes that he sells. How many shoes would Bob have sell in he wants to earn $2000.00 a week? How much money would Bob get if he sells 100 shoes and works for 50 hours? [BThevakumar]

52. A party is filled with an equal number of boys and girls. Five boys left at nine o'clock, leaving twice as many boys as girls. What was the original number of friends at the party? [kobeaswaran]

53. Carolyn, Melissa, Areej and Eleanor have a box of cookies. The cookies are divided 1:2:4:5. There are 24 cookies in the box. How many cookies does each person receive? [carolyntait]

54. The speed of light is 299 792 458 metres per second and the speed of sound is 343 metres per second. If light travels left from a certain point and sound travels right from the same point, then calculate the total distance in metres that light and sound have travelled after 2.5 minutes. [kevink2435]

55. Steven has a pocket full of change in quarters and dimes only. He has a total of $5.40. The amount of dimes are twice as much as the quarters. How many dimes and quarters does Steven have? [m_sanghvi, l_leung and YYuan]

56. Hints: The formula for the line formation is: y=mx+b, where m is the slope and b is the y-intercept. You can use one of the sets of ordered pairs to substitute values for the x- and y- variables.

A line passes through point A(2, -4) and point B(4,-8). Write an equation for the y-variable in terms of the x-variable; in other words, write the complete formation formula for this line.

[kevink2435]

57. A line passes through point A(3,0) and point B(3,3). Is it possible to calculate the slope of this line? If not, explain why. [kevink2435]

58. A line passes through point A(0,3) and point B(2,3). Is it possible to calculate the slope of this line? If so, explain why it has a slope of 0. [kevink2435]

59. The formula for line formation is: y=mx+b, where m is the slope and b is the y-intercept. If m>0 and b>0, then how many quadrants would this line pass through on the graph? Identify the quadrants. [kevink2435]

60. The line formation of one line is y=mx+3, where m is the slope and 3 is the y-intercept. The line formation of another line is y=-4x+b, where -4 is the slope and b is the y-intercept. If both of these lines pass through point (-1,5), then solve for m+b.

[kevink2435]

61. Two lines on a graph have the same slope but different y-intercepts. Are the lines parallel to each other? If so, explain why.

[kevink2435]

62. Cleo, Ramya and Jennifer all went to the Stitches warehouse in Barrie. Ramya spent five times of what Cleo spent. Jennifer spent one third of what Cleo spent. They spent a total of $76.00 on their purchases at the warehouse. How much did Jennifer spend? [tnagendrasooriyar]

63. At 11:00 a.m., Ron started driving along a highway at constant speed of 50km / hour. A quarter of an hour later, Edward started driving along the same highway in the same direction as Ron at the constant speed of 65km / hour. At what time will Edward catch up with Ron? [Kopeaswaran]

64. The numbers 2, 3 , 5 and x have an average equal to 4. What is x? [Kopeaswaran]

65. The ratio of the cost of Dial hand soap to Dove hand soap is 6:4, and the cost of Dove hand soap is $4.20. What would be the cost of the Dial hand soap? [eyip]

66. The ratio of votes for Lisa to votes for Jack in a student council election campaign is 20: 14. There were a total of 170 votes altogether. How many people voted for Jack during the election? [m-yang, aashraf1]

67. What amount of money was invested at 8% compounded annually will grow to $5, 000 in 5 years? [Slakkunarajah]

68. The number of ants in a colony doubles every month from now. If there are now 1000 ants in the colony, about how many will there be half a month from now? How many were there a half month ago? [Slakkunarajah]

69. How long will it take $1000 to grow to $1500 when it is invested at 8% compounded annually? [Slakkunarajah]

70. Convert 4x-9/2y+33=0 into slope-y-intercept form. [kevink2435]

71. Find the slope-y-intercept of the line through the points (-5, 10) and (10,-7). [Slakkunarajah]

72. Write an equation of the line in y=mx=b. Then, write the equation in standard form, for the given. m= 2/3 b= -1 [Slakkunarajah]

73. There are around 500 wolves in Algonquin Provincial Park,Ontario. Every 35 years, this population doubles under ideal conditions. a) What is the possible wolf population of the Park in: i) 10 years? ii) 50 years? b) How were there: i) 10 years ago? ii) 20 years ago? [Slakkunarajah]

74. The area of a British Colombia flag can be represented by the expression 2x² + 4x + 2 and its width by x + 1. a) Write and simplify an expression for the length. b) Write and simplify an expression that represents the ratio length: width for a British Colombia flag. [Slakkunarajah]

75. In 2007, the number of students in a school is 80 more than the number of staff members. In 2012, the number of students decreased by 25% and the number of staff members increased by 20% causing the number of staff members to exceed the number of students by 30.

a) What is the rate of change for the students? b) What is the rate of change for the staff? c) How many students were there in 2007? d) How many staff members were there in 2012? [//hli//]


 * __Challenging Questions__

Challenge Question #1**

Find a number which decreased by 18 is 5 times its opposite.

[pjvasdev]


 * Challenge Question #2**

A vendor sells hot dogs, hamburgers, and sausages. A customer buys 4 hot dogs, 5 hamburgers, and 4 sausages for $30.66. The price of a hot dog is $12.00 more than the price of a hamburger. The price of a sausage is $2.00 less than the price of 5 hamburgers. Find the cost of each item.

[kevink2435]


 * Challenge Question #3**

If Kevin earns $132/ 9h, how much does he earn in 20h?

[kevink2435]


 * Challenge Question #4**

Brandon works in a shoe-selling store. He earns $1299/week, plus a commission of 20% of his sales. a) write the partial variation equation to describe his earning in one week. b) Graph this equation c) Using the pattern that you just found in the graph, if Brandon earned $100 000 000 in one week, what is the total value for all the shoes he sold?

[kevink2435]


 * Challenge Question #5**

The formula for volume is: V=lwh. Is this equation a direct variation or a partial variation? Explain your reason.

[kevink2435]


 * Challenge Question #6**

Write 3²+3²+3² as a power of 3.

[kevink2435]


 * Challenge Question #7**

In 2007, the number of students in a school is 80 more than the number of staff members. In 2012, the number of students decreased by 25% and the number of staff members increased by 20% causing the number of staff members to exceed the number of students by 30.

a) What is the rate of change for the students? b) What is the rate of change for the staff? c) How many students were there in 2007? d) How many staff members were there in 2012? [//hli//]


 * Challenge Question #8**

For the first 5 seconds, Kevin can run at a speed of 25 km/h. If his rate of speed drops continuously by 2 km/h every 5 seconds, then what's the total distance in kilometres that he ran before he came to a stop?

[kevink2435]


 * Answers are on Word Problems (Answers) page!