Real world examples of systems of equations

  1. Adhiti bought 6 tickets to a football game & spent $34. He bought a combination of student tickets for $4 each and adult tickets for $9 each. Determine the number of adult and student tickets he bought?
  1. When a small boat travels downstream, it can travel 10 miles in 3 hours. When the same boat travels the opposite direction against the flow, it takes 5 hours to travel the same distance. Find the average rate of the boat in still water and the average rate of the water.
  1. You sold 52 boxes of candy for your marching band fundraiser. The large size box costs $3.50 each and the small size box costs $1.75 each. If you sold $112.00 worth of candy, how many large boxes of candy did you sell?
  1. A history test is to have 20 questions. The teacher uses multiple choice and essay questions. The multiple choice questions are worth 4 points each and the essay questions are worth 8 points each. The test has a total of 100 points. Determine how many of each type of question appears on the test.
  1. You are planning a birthday party for your younger brother at a skating rink. The cost of admission is $3.50 per adult and $2.25 per child, and there is a limit of 20 people. You have $50 to spend. Determine how many adults and children you can invite?
  1. Selling frozen yogurt at a fair, you make $565 and use 250 cones. A single-scoop cone costs $2 and a double-scoop cone costs $2.50. How many of each type of cone did you sell?
  1. Flying with the wind, a plane flew 600 miles in 3 hours. Flying against the wind, the plane could fly only 300 miles in the same amount of time. Find the speed of the plane in calm air and the speed of the wind.
  1. A chemist working on a flu vaccine needs to mix a 10% sodium-iodine solution with a 60% sodium-iodine solution to obtain 50 milliliters of a 30% sodium-iodine solution. How many milliliters of the 10% solution and of the 60% solution should be mixed?
  1. Lawrence HS prevailed in Saturday’s track meet with the help of 20 individual-event placers earning a combined 68 points. A first-place finish earns 5 points, a second-place finish earns 3 points, and a third-place finish earns 1 point. Lawrence HS had a strong second-place showing, with as many second-place finishers as first- and third-place finishers combined. Determine the number of finishers in each position.