# Questions on Word Problems: Linear Equations And Systems Word Problems answered by real tutors!

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 Linear Solvers Practice Answers archive Word Problems Lessons In depth

 Question 167491: there are 3 times as many cars as motorcycles. there are a total of 28 tires. How many motorcycles are there? Click here to see answer by Mathtut(3670)

 Question 167517: Tickets for adults are 5.50 and tickets for children are 3.50. How many of each kind of ticket was purchased if 21 tickets were bought for 83.50? Click here to see answer by checkley77(12569)

 Question 167610: 1. The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for \$5 per pound with some Orange Pekoe tea that sells for \$3 per pound to get 100 pounds of the new blend. The price of the new blend is to be \$4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and the Orange Pekoe tea are required? I'm in pre-calculus and this was a problem that was given to us. I understand that it's a system of linear equations, but I just can't seem to set the 2 equations up right. I was thinking the two equations would be: x+y=100; 5x+3y=4.50 but it just doesn't come out right. Any help on how to set up the equations would be great! Thanks. Click here to see answer by Mathtut(3670)

 Question 167631: Mr.La Fleur pays \$130 to rent a car for one week. He also pays \$5 for every 100 miles that he drives. Write an equation and draw a graph which shows the relationship between the total cost of renting the car and the number of miles that are driven. Click here to see answer by Mathtut(3670)

 Question 167692: sam has 30 nickles and dimes worth \$2.40. How many nickles does he have? Click here to see answer by nerdybill(7003)

 Question 167720: a natural food store makes its own brand of trial mix, out of dried apples,raisins and peanuts. One pound of the mixture is \$3.18 it contains twice as much peanuts by weight than apples. One pound of dried apples cost \$4.48, a pound of raisins cost \$2.40 and a pound of peanuts is \$ 3.44. How many ounces of each ingredient are contained in one pound of the trail mix? Click here to see answer by ankor@dixie-net.com(15746)

 Question 167760: john has retired and needs \$ 6000 per annum to live. he has \$50000 to invest and can invest in bonds at 15 % annual interest or in bank certificates at an annual rate of 7 % .how much money should he invest in each type of investment to get a income of 6000 \$ per annum? what if he determines he actually requires an income of 7000 per year Click here to see answer by checkley77(12569)

 Question 167777: In Florida, when there were 447 boats registered (in thousands) there were 13 manatees killed that year. During a year when there were 719 boats registered (in thousands) there were 47 manatees killed that year. Assuming a linear relationship between boats registered and manatees killed, find a linear equation that describes the number of manatees killed with respect to boats registered. (discuss the meaning of the slope for this problem). Click here to see answer by stanbon(57962)

 Question 168227: A manufacturer of custom drinking mugs has the capacity to produce 1,800 mugs per day. It has a fixed daily cost of \$1,000 plus a variable cost of \$1.50 per mug. a)How many mugs were created in a batch that had a total daily cost of \$2,800? b)The total cost of mugs can also be calculated by multiplying the average cost per mug by the number of mugs produced. If the company needs to reach an average cost of \$2.00 per mug, how many mugs must it produce per day? Click here to see answer by hobbitt(2)

 Question 168226: A bricks manufacturer has daily costs \$180 and a variable cost of \$1.50 per brick. Determine how many bricks the company needs to make per day to meet its goal of an average cost of \$2.00 per brick. Note that the total cost can also be calculated by multiplying the average cost per brick by the number of bricks produced Click here to see answer by 303795(595)

 Question 168295: The width of a rectangle is 12 units less than the length. The perimeter is 108 units. Find the length. Click here to see answer by checkley77(12569)

 Question 168436: the width of a rectangle is 3ft less than the length. The perimerter is 62ft. Find the length and the width of the rectangle. Click here to see answer by midwood_trail(310)

 Question 168521: A jar containing pennies, nickels and dimes is worth \$8.40. The number of dimes is six less than twice the number of pennies and there is an equal number of dimes and nickels. How many nickels are in the jar. Click here to see answer by Mathtut(3670)
 Question 168521: A jar containing pennies, nickels and dimes is worth \$8.40. The number of dimes is six less than twice the number of pennies and there is an equal number of dimes and nickels. How many nickels are in the jar. Click here to see answer by josmiceli(9817)

 Question 168555: An office manager is purchasing file cabinets and wants to maximize storage space. The office has 60 square feet of floor space for the cabinets and \$600 in the budget to purchase them. Cabinet A requires 3 square feet of floor space, has a storage capacity of 12 cubic feet, and costs \$75. Cabinet B requires 6 square feet of floor space, has a storage capacity of 18 cubic feet, and costs \$50. How many of each cabinet should the office manager buy? Solve using the substitution method. Click here to see answer by Mathtut(3670)

 Question 168592: 1. The length of a rectangle is three times the width. The area is 108in^2. Find the length and the width. is six. The sum of the squares of the two numbers is twenty-six. Find the two numbers.2. The sum of two numbers Click here to see answer by iluvbuilding429(41)

 Question 168630: The perimeter of a rectangle is 20 meters. If the length is increased by four times the width, the sum is 19 meters. What are the dimensions of the rectangle? What is its area? Click here to see answer by ankor@dixie-net.com(15746)

 Question 168697: an average score of 90 or above in an english course receives an A grade. a student has grades of 85, 88, 90, and 98 on four tests. find the range of scores on the fifth test that will give the student an A grade Click here to see answer by jojo14344(1512)

 Question 167811: Need help graphing this equation. Find the dimensions of the rectangular field of maximum area which can be enclosed with 400 feet of fence. The vertex is (100, 10000), -w^2+200w and the parabola would be downward, but when I put the equation in my calulator. I do not see the parabola. Click here to see answer by 303795(595)

 Question 169384: A car rental company has two rental rates. Rate 1 is \$72 per day plus \$0.16 per mile. Rate 2 is \$144 per day plus \$0.08 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2? Click here to see answer by Mathtut(3670)

 Question 169649: Javier is on a diet. He is supposed to eat at least 1500 but not more than 1800 calories per day. Before his last meal of the day, he had consumed 1150 calories. According to Javier's diet plan, what number of calories may he consume at his last meal of the day? Please show all work. Thank you very much!! Click here to see answer by Mathtut(3670)

 Question 169697: I need help. I have been trying to work this problem for several days and I am confused. This is the problem: The Johnson family is planning a weeklong vacation in California and needs to rent a car. They don't know exactly how far they will drive, but they estimate between 400 and 800 miles. Here are the options: Weekly Rates: \$329 per week, unlimited mileage or \$219 per week, plus 12 cents per mile. Daily Rates: \$50 per day, unlimited mileage or \$40 per day, plus 3 cents per mile. Write the total week's rental car cost as a function of the number of miles driven in a week for each of the options. The costs of each option must also be represented on a data table and then graphed to show the cost of each option. Click here to see answer by gonzo(654)

 Question 169777: The cost in dollars, C, to produce x books is given by C(x)=1.05x+230. The ordered pair (100,335) is a solution of the equation. Which of the following sentences describes this ordered pair? A.) It costs \$100 to produce 335 books. B.) It costs \$335 to produce 100 books. C.) 100 books can be sold for \$335. D.) 335 books can be sold for \$100. Click here to see answer by jim_thompson5910(28715)
 Question 169777: The cost in dollars, C, to produce x books is given by C(x)=1.05x+230. The ordered pair (100,335) is a solution of the equation. Which of the following sentences describes this ordered pair? A.) It costs \$100 to produce 335 books. B.) It costs \$335 to produce 100 books. C.) 100 books can be sold for \$335. D.) 335 books can be sold for \$100. Click here to see answer by edjones(7569)

 Question 169808: The problem: Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution. Ms. Jones purchased a total of \$45,000 in stocks, bonds, and money market funds. The total she invested in bonds and money market funds was twice the amount she invested in stocks. The return rates on the stocks, bonds, and money market funds were 10.0%, 7.0%, and 7.5%, respectively. The total value of the return was \$3,660. How much of each investment (stocks, bonds, and money market funds) did Ms. Jones purchase? My attempt: 2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks) x(10%) + x(7%) + x(7.5%) =3600 Solving the first equation I get: 5x = 4500; x = 9000 plug the value for x back into the equation and it adds up. ( 5 * 9000= 45000) Insert the values of x into the second equation and it does not add up. (9000 * 10%) + (18000 * 7%) + (18000 * 7.5) = 3510 The answer is off by \$150 (3660 - 3510 = 150) Am I reading this word problem wrong? Click here to see answer by stanbon(57962)
 Question 169808: The problem: Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution. Ms. Jones purchased a total of \$45,000 in stocks, bonds, and money market funds. The total she invested in bonds and money market funds was twice the amount she invested in stocks. The return rates on the stocks, bonds, and money market funds were 10.0%, 7.0%, and 7.5%, respectively. The total value of the return was \$3,660. How much of each investment (stocks, bonds, and money market funds) did Ms. Jones purchase? My attempt: 2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks) x(10%) + x(7%) + x(7.5%) =3600 Solving the first equation I get: 5x = 4500; x = 9000 plug the value for x back into the equation and it adds up. ( 5 * 9000= 45000) Insert the values of x into the second equation and it does not add up. (9000 * 10%) + (18000 * 7%) + (18000 * 7.5) = 3510 The answer is off by \$150 (3660 - 3510 = 150) Am I reading this word problem wrong? Click here to see answer by solver91311(17077)
 Question 169808: The problem: Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution. Ms. Jones purchased a total of \$45,000 in stocks, bonds, and money market funds. The total she invested in bonds and money market funds was twice the amount she invested in stocks. The return rates on the stocks, bonds, and money market funds were 10.0%, 7.0%, and 7.5%, respectively. The total value of the return was \$3,660. How much of each investment (stocks, bonds, and money market funds) did Ms. Jones purchase? My attempt: 2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks) x(10%) + x(7%) + x(7.5%) =3600 Solving the first equation I get: 5x = 4500; x = 9000 plug the value for x back into the equation and it adds up. ( 5 * 9000= 45000) Insert the values of x into the second equation and it does not add up. (9000 * 10%) + (18000 * 7%) + (18000 * 7.5) = 3510 The answer is off by \$150 (3660 - 3510 = 150) Am I reading this word problem wrong? Click here to see answer by gonzo(654)

 Question 169469: The ratio of jeeps is green to black 5 to 2. If green jeeps consume 800,000 gallons of fuels and black jeeps consume 1,100,000 gallons. If there was 18600,000 gallons of fuel how many green and black jeeps are there. Click here to see answer by jojo14344(1512)

 Question 169821: Ken mails three packages at the post office that weigh 8.1, 8.5, and 8.9 lbs. The post office that Ken uses rounds the weight of a package to the nearest pound to determine the price of shipment It costs \$2 to mail a package that weighs 8 pounds and \$2.75 for packages that weigh 9 lbs. a. How much did Ken pay to ship each package? b. Ken has \$7.25 in his wallet in cash. Use subtraction to determine whether Ken has enough to mail the three packages and how much extra money he has or needs. Click here to see answer by stanbon(57962)

 Question 170165: 1. A lawyer bills her clients \$200 per hour of service. If a client's case requires 39 hours to complete, use proportion to calculate how much the client will owe the lawyer (excluding tax). Click here to see answer by jim_thompson5910(28715)

 Question 170192: Can someone help? A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep? Click here to see answer by nerdybill(7003)

 Question 170382: 3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M. The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N. a. Form the equations of both the lines. Show your work. b. What are the co-ordinates of the point of intersection of lines M and N? c. Write the co-ordinates of the intersections of lines M and N with the x-axis. d. Write the co-ordinates of the intersection of lines M and N with the y-axis. Click here to see answer by checkley77(12569)

 Question 170454: Hi, Here's my fourth and final GRE math prep word problem of the day: If 3 time's Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between their ages is 15 years, how old are Jane and Beth? Thank you, Julie Click here to see answer by nerdybill(7003)

 Question 170647: A rectangular light switch plate is made according to the following dimensions. The length is 7 inches, and the width is 5.5 inches: a rectangular hole measuring 1.2 inches by 0.3 inches is left in the center. A) How many square inches in area is the light-switch plate( the shaded region)? B) If the cost to construct the plate is \$4.27 per square inch, What is the construction cost? I used formula A=LW (17in)(5.5in)=93.5 shaded part (1.2in)(0.3in)= .36in From there I don't know what to do? Click here to see answer by Mathtut(3670)

 Question 170741: Two plates and a cup together weigh more than three goblets, whereas two goblets and a cup weigh more than two plates. Does a goblet weigh more or less than two cups? I'm not sure how to approach this question... do I assign a variable to each unknown? Or use one variable? Then do I solve using the substitution method or...? I'm lost! help! Click here to see answer by Fombitz(13828)

 Question 170766: The equation for the cost in dollars of producing automobile tires is 2 C=0.000015x -0.03+35, where x is the number of tires produced. Find the number of tires that minimizes the cost. What is the cost for that number of tires? ***note the 2 in the second row means that 0.000015x is squared Click here to see answer by nerdybill(7003)

 Question 170863: what to do? please help..find the GCF of the terms of each polynomial. Factor. upward arrow means exponent t^6 + t^4 - t^5 + t^2 Click here to see answer by jim_thompson5910(28715)

 Question 170697: The sum of two numbers is 175. The larger number is three more than three times the smaller number. Write a system of equations and solve the system to find the numbers. Please help Thanks Jason Click here to see answer by Mathtut(3670)
 Question 170697: The sum of two numbers is 175. The larger number is three more than three times the smaller number. Write a system of equations and solve the system to find the numbers. Please help Thanks Jason Click here to see answer by KnightOwlTutor(293)