curiouskids

Algebra test prep

Due: Jul 26th

Questions

  1. Solve the system of equations: 3x + 4y = 17 2x - 3y = 6
  2. Solve the equation for y: 5x - 2y = 10
  3. Solve the inequality: 3x - 5 > 2(x - 3) + 7
  4. If a car uses 5 liters of fuel for 60 kilometers, how much fuel will it use for 450 kilometers?
  5. The sum of two numbers is 50 and their difference is 10. What are the numbers?
  6. How much pure acid should be added to 500 ml of a 30% acid solution to increase its concentration to 50%?
  7. If you jog at 6 km/h, how far can you go in 30 minutes?
  8. A train travels at an average speed of 60 km/h. How long will it take to travel 360 kilometers?
  9. Solve for x: 4x^2 - 9 = 0
  10. The sum of the angles in a polygon is 1260 degrees. How many sides does the polygon have?
  11. Simplify the expression: (3x^2 - 2x + 1) - (2x^2 - 3x + 2)
  12. You invested $5000 between two accounts. The first account pays 3% annual interest and the second pays 5% annual interest. If you earned $210 in interest after one year, how much did you invest in each account?

Solutions

  1. The system of equations 3x + 4y = 17 2x - 3y = 6 can be solved using substitution or elimination methods to yield x = 3 and y = 2.

  2. To solve 5x - 2y = 10 for y, you rearrange it to get y = (5x - 10) / 2.

  3. Solving the inequality 3x - 5 > 2(x - 3) + 7 gives x > 4.

  4. If a car uses 5 liters of fuel for 60 kilometers, it will use 5 * (450 / 60) = 37.5 liters for 450 kilometers.

  5. Let’s denote the two numbers as x and y. From x + y = 50 and x - y = 10, solving these equations gives x = 30 and y = 20.

  6. Let’s denote the amount of pure acid to add as x (in ml). The equation is 500 * 0.30 + x = (500 + x) * 0.50. Solving for x gives x = 200 ml.

  7. If you jog at 6 km/h, in 30 minutes (or 0.5 hours) you can go 6 * 0.5 = 3 km.

  8. If a train travels at an average speed of 60 km/h, it will take 360 / 60 = 6 hours to travel 360 kilometers.

  9. Solving for x in 4x^2 - 9 = 0 gives x = 1.5 and x = -1.5.

  10. The sum of the angles in a polygon is 180(n - 2) degrees, where n is the number of sides. Solving 180(n - 2) = 1260 gives n = 9, so the polygon has 9 sides.

  11. Simplifying the expression (3x^2 - 2x + 1) - (2x^2 - 3x + 2) gives x^2 + x - 1.

  12. Let’s denote the amount invested in the first account as x and in the second account as 5000 - x. The equation is 0.03x + 0.05(5000 - x) = 210. Solving for x gives x = 3000. Therefore, $3000 was invested in the first account and 5000 - 3000 = 2000 was invested in the second account.

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