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Math Problems and Equations for Students

A set of math problems and equations for students to solve, covering topics such as algebra, linear equations, and projections.

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Math Problems and Equations for Students

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  1. A recycling center pays $0.35 per pound of glass that it receives. If students at Falcon High School want to raise $500 in a glass-recycling project, what is a reasonable number of pounds of glass they must collect? A 750 lb B 175 lb C 500 lb D 1500 lb Problem #1 Obj 4 - TAKS 2004 9th [A.C3(C)]

  2. A weather balloon is launched from a height of 475 feet above sea level. If the balloon rises at a constant rate of 85 feet per minute, which equation could be used to determine t, the time in minutes it will take the balloon to reach a height of 9245 feet above sea level? A 9245 = 85 + 475t B 9245 = 85(t + 475) C 9245 = 475 + 85t D 9245 = (475 + 85)t Problem #2 Obj 4 - TAKS 2004 9th [A.C3(A)]

  3. If (x, –4) is a solution to the equation 4x – 5y = 8, what is the value of x? A –4.8 B –3 C 1.6 D 7 Problem #3 Obj 4 - TAKS 2004 9th [A.C3(B)]

  4. The graphs of the linear equations y = 2x – 3 and y = 3x – 7 are shown to the right. If 2x – 3 = 3x – 7, what is the value of x? A 4 B 5 C 9 D 10 Problem #4 Obj 4 - TAKS 2004 9th [A.C3(B)]

  5. A shaded parallelogram is graphed on the coordinate grid to the right. Which of the following functions describes a line that would include an edge of the shaded parallelogram? A y = –2x + 5 B y = –2x – 2 C y = –2x + 9 D y = –2x – 1 Problem #5 Obj 4 - TAKS 2004 10th [A.C3(A)]

  6. What is the x-coordinate of the solution to the system of linear equations below? 4x + 5y = 8 2x – 3y = –18 A –4 B –3 C 3 D 4 Problem #6 Obj 4 - TAKS 2004 10th [A.C4(B)]

  7. In 1998 the enrollment at a community college was approximately 2500 students. In 2002 the enrollment had increased to 3250 students. If the enrollment continues to increase at this rate, what is a reasonable projection of enrollment for 2010? A 4750 B 5750 C 6250 D 9000 Problem #7 Obj 4 - TAKS 2004 10th [A.C3(C)]

  8. Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g? A 5f + 3g = 3.60 2f + 10g = 5.70 B 5f + 2g = 5.70 3f + 10g = 3.60 C f + g = 22 7f + 13g = 9.30 D 5f + 3g = 5.70 2f + 10g = 3.60 Problem #8 Obj 4 - TAKS 2004 10th [A.C4(A)]

  9. Rita put some hummingbird feeders in her backyard. The table shows the number of hummingbirds that Rita saw compared to the number of feeders. Which equation best describes the relationship between h, the number of hummingbirds, and f, the number of feeders? A h = 2f + 1 B f = 2h + 1 C h = f + 2 D Problem #9 Obj 4 - TAKS 2004 10th [A.C3(A)]

  10. The graph of the equation is given to the right. Graph y = x + 1 on the grid. What is the solution to this system of equations? A (0, 1) B (5, 6) C (6, 7) D No solution Problem #10 Obj 4 - TAKS 2004 11th [A.C4(B)]

  11. At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book? A m + n = 8 m = 3n + 54 B m + n = 8 m = 3n – 54 C m + n = 54 m = 3n+ 8 D m + n = 54 m = 3n – 8 Problem #11 Obj 4 - TAKS 2004 11th [A.C4(A)]

  12. The amount of an employee’s weekly pay, p, including a bonus, can be represented by the inequality 6.00h + 100 < p < 6.50h + 125, where h represents the number of hours worked by the employee. If an employee worked 25 hours, which of the following is a reasonable amount for that week’s pay? A $118.75 B $250.00 C $272.50 D $290.25 Problem #12 Obj 4 - TAKS 2004 11th [A.C3(C)]

  13. The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store? A 2e – u = 220 e – u = –175 B 2e – u = 220 e + u = 175 C 2e – 2u = 440 e – u = –175 D e – 2u = –220 e – u = 175 Problem #13 Obj 4 - TAKS 2004 11th [A.C4(A)]

  14. Ms. Barton determined that the total cost of her wedding, c, could be represented by the equation c = 75n + 1500, where n is the number of people attending the wedding. If Ms. Barton’s wedding cost $8625, how many people attended the wedding? A 135 B 95 C 115 D 75 Problem #14 Obj 4 - TAKS 2004 11th [A.C3(B)]

  15. Auto-Check Motors charged Mr. Jones $84.00 for an automotive part plus $68.00 per hour that a mechanic worked to install the part. The total charge was $353.00. For about how long did the mechanic work to install the part on Mr. Jones’s car? A. 6 hours B. 5 hours C. 4 hours D. 3 hours Problem #15 Obj 4 - TAKS 2003 9th [A.C3(B)]

  16. The number of hours Abe practices golf each week, g, is 2 more than the number of hours he runs, r. Which equation represents the number of hours he runs each week? A. r = g – 2 B. g = r – 2 C. g = 2r D. r = g + 2 Problem #16 Obj 4 - TAKS 2003 9th [A.C3(A)]

  17. Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 108 CDs over the two weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week? A. l + t = 108 t = 3l + 6 B. l + t = 108 t = 3l – t C. l + t = 108 l = 3t – 6 D. l + t = 108 l = 3t + 6 Problem #17 Obj 4 - TAKS 2003 9th [A.C4(A)]

  18. The cost of renting a DVD at a certain store is described by the function f(x) = 4x + 3 in which f(x) is the cost and x is the time in days. If Lupe has $12 to spend, what is the maximum number of days that she can rent a single DVD if tax is not considered? A. 1 B. 2 C. 3 D. 7 Problem #18 Obj 4 - TAKS 2003 9th [A.C3(C)]

  19. Passengers on many commercial flights may make calls from a telephone provided by the airline. On a certain airline a call costs $3 to connect plus $2 for each minute. Which equation best represents c, the total cost for a call that lasts m minutes? A. m = 3 + 2c B. c = 3 + 2m C. m = 2 + 3c D. c = 2 + 3m Problem #19 Obj 4 - TAKS 2003 9th [A.C3(A)]

  20. At Northwest Electronics audiotapes cost $5.00 per package, and videotapes cost $10.00 per package. Which inequality best describes the number of packages of audiotapes, a, and the number of videotapes, v, that can be purchased for $45.00 or less? A. 5a + 10v < 45 B. 10a + 5v ≤ 45 C. 5a + 10v ≤ 45 D. 10a + 5v < 45 Problem #20 Obj 4 - TAKS 2003 10th [A.C3(A)]

  21. The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters? A. l = w + 3 2(l + w) = 85 B. l = 3w 2l + 6w = 85 C. l = 3w 2(l + w) = 85 D. l = w + 3 2l + 6w = 85 Problem #21 Obj 4 - TAKS 2003 10th [A.C4(A)]

  22. What is the value of y if (3, y) is a solution to the equation 5x – 3y = 18? A. 3 B. 1 C. –1 D. –11 Problem #22 Obj 4 - TAKS 2003 10th [A.C3(B)]

  23. Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a systems of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution? A. (6, 9) B. (5, 10) C. (9, 6) D. (10, 5) Problem #23 Obj 4 - TAKS 2003 10th [A.C4(B)]

  24. Which graph best represents a solution to this system of equations? 2x – 3y = 0 x + 2y = –7 Problem #24 Obj 4 - TAKS 2003 10th [A.C4(B)]

  25. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk? A. t + m = 2.10 2t + 2m = 5.15 B. t + m = 2.10 3t + 3m = 5.15 C. t + m = 2.10 3t + 2m = 5.15 D. t + m = 2.10 2t + 3m = 5.15 Problem #25 Obj 4 - TAKS 2003 11th [A.C4(A)]

  26. Anna makes hand-painted plates. Her overhead costs are $750 per week, and she pays an additional $10 per plate in material costs. If Anna sells the plates for $25 each, how many plates does she have to sell each week before she can make a profit? A. 20 B. 30 C. 50 D. 75 Problem #26 Obj 4 - TAKS 2003 11th [A.C3(B)]

  27. At a firefighters’ pancake breakfast, the firefighters served 345 people and raised $1395. If the cost of a, an adult’s ticket to the pancake breakfast, was $5 and the cost of c, a child’s ticket, was $3, what was the number of adult tickets sold? A. 165 B. 180 C. 279 D. 345 Problem #27 Obj 4 - TAKS 2003 11th [A.C4(B)]

  28. On Wednesdays an athlete’s schedule allows no more than 75 minutes for morning training. One round of a strength routine, s, requires 8 minutes. One round of an endurance routine, e, requires 12 minutes. Which of these best represents the time available for the athlete to spend on strength and endurance routines on Wednesdays? A. 20(s + e) > 75 B. 8s = 75 – 12e C. 8s + 12e ≤ 75 D. 12e < 75 + 8s Problem #28 Obj 4 - TAKS 2003 11th [A.C3(A)]

  29. Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polish at $2 each. She spent less than $12, not including tax. Use the grid to the right to graph the inequality 4x + 2y < 12. Which point represents a reasonable number of lipsticks and bottles of nail polish that Valerie purchased? A. (1, 5) B. (2, 3) C. (1, 3) D. (2, 2) Problem #29 Obj 4 - TAKS 2003 11th [A.C3(C)]

  30. If (x, −3.2) is a solution to the equation 4x = 5y − 17, what is the value of x? F. 0.84 G. 0.25 H. −5.96 J. −8.25 Problem #30 Obj 4 - TAKS 2006 9th [A.C3(B)]

  31. Harris has $20.92 to spend on video-game rentals at a local video store. The store charges $3.95 per video-game rental plus an 8.125% tax. What is the maximum number of video games that Harris can rent? A. 5 B. 4 C. 6 D. 3 Problem #31 Obj 4 - TAKS 2006 9th [A.C3(C)]

  32. The perimeter of a rectangular wooden deck is 90 feet. The deck’s length, l , is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck? F. 2l + 2w = 90 l = 5 – 4w G. 2l + 2w = 90 l = 5w – 4 H. 2l + 2w = 90 l = 4 – 5w J. 2l + 2w = 90 l = 4w – 5 Problem #32 Obj 4 - TAKS 2006 9th [A.C4(A)]

  33. Brandon has a budget of $58 to spend on clothes. The shirts he wants to buy are on sale for $9 each, and the pair of pants he wants costs $21. All prices include tax. Which inequality could be used to determine s, the maximum number of shirts Brandon can buy if he also buys the pair of pants? F. 21s + 9 < 58 G. 9s + 21 58 H. 30s < 58 J. 9s − 21 58 Problem #33 Obj 4 - TAKS 2006 9th [A.C3(A)]

  34. A florist plans to sell bouquets for $25 each. He wants to use only roses and carnations in each bouquet and needs to charge the following amount for each type of flower. $1.50 per rose $1.25 per carnation Which of these combinations of roses and carnations will result in bouquets that the florist can sell for exactly $25 each? I. 18 roses and 2 carnations II. 6 roses and 10 carnations III. 10 roses and 8 carnations IV. 5 roses and 14 carnations F. I and II only G. II and III only H. III and IV only J. I and IV only Problem #34 Obj 4 - TAKS 2006 9th [A.C3(C)]

  35. In 2004 a married couple could have calculated their estimated income tax, t, for that year using the equation t = 0.25c − 6525, in which c represents their combined taxable income. If a married couple had a combined taxable income between $60,000 and $64,000, which of the following is a reasonable amount for their income tax? F. $6,525 G. $8,975 H. $13,869 J. $15,500 Problem #35 Obj 4 - TAKS 2006 10th [A.C3(C)]

  36. Norma and Lauretta went to a store to buy DVDs on sale • for $5 each, tax included. Norma purchased two and a half • times as many DVDs as Lauretta purchased. Together they • purchased 14 DVDs. Which system of linear equations can • be used to determine n, the number of DVDs Norma purchased, and l, the number of DVDs Lauretta purchased? • n + l = 14 • n = ½ l • G. 5n + 5l = 14 • l = ½ n • H. n + l = 14 • n = l • J. n + l = 14 • l = n Problem #36 Obj 4 - TAKS 2006 10th [A.C4(A)]

  37. The length of each leg of an isosceles triangle is 5 centimeters more than twice the length of the base. If the perimeter of this isosceles triangle is 95 centimeters, what is the length of the base? A. 17 cm B. 21 cm C. 30 cm D. 39 cm Problem #37 Obj 4 - TAKS 2006 10th [A.C3(B)]

  38. If the system of linear equations 2x + y = 1 and y = − ½ x + 1 are graphed on the same coordinate grid, which of the following is the solution to this system of linear equations? A. (2, 0) B. (0, 2) C. (0.5, 0) D. Not here Problem #38 Obj 4 - TAKS 2006 10th [A.C4(B)]

  39. A chemist started an experiment with 5 grams of a chemical. The chemical was used at a rate of 0.01 gram per minute. Which equation best describes the relationship between c, the amount of chemical remaining in grams, and t, the time in minutes? F. c = 5.01t G. c = 4.99t H. c = 5 − 0.01t J. c = 0.01t − 5 Problem #39 Obj 4 - TAKS 2006 10th [A.C3(A)]

  40. The student council at Jefferson High School sold a total of 220 brownies and cookies during its fund-raiser. Each brownie sold for $0.75, and each cookie sold for $0.50. The student council made $136.50 from the sales of brownies and cookies. Which system of linear equations can be used to find b, the number of brownies sold, and c, the number of cookies sold? A. b + c = 220 0.50b + 0.75c = 136.50 B. b + c = 136.50 0.75b + 0.50c = 220 C. b + c = 136.50 0.50b + 0.75c = 220 D. b + c = 220 0.75b + 0.50c = 136.50 Problem #40 Obj 4 - TAKS 2006 11th [A.C4(A)]

  41. A salesclerk earns $250 per week plus a commission of of her total sales. If her sales total x dollars, which equation can be used to determine her total weekly earnings? A. y = 250(x + ) B. y = 250x + x C. y = 250x + D. y = 250 + x Problem #41 Obj 4 - TAKS 2006 11th [A.C3(A)]

  42. The equation F = C + 32 represents the relationship between F, the temperature in degrees Fahrenheit, and C, the temperature in degrees Celsius. If the temperature is 104°F, what is the temperature in degrees Celsius? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Problem #42 Obj 4 - TAKS 2006 11th [A.C3(B)]

  43. The graph of a system of linear equations is shown below. Which of the following is the solution to this system of linear equations? F. (0, 4) G. (8, 1) H. (0, −3) J. (10, 2) Problem #43 Obj 4 - TAKS 2006 11th [A.C4(B)]

  44. Lisa wants to make a long-distance telephone call to her friend. She does not want to spend more than $5.00 on the telephone call. If there is a $0.50 connection fee and a charge of $0.11 per minute, which best represents the number of minutes that Lisa can talk to her friend? A. B. C. D. Problem #44 Obj 4 - TAKS 2006 11th [A.C3(C)]

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