A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 poin

May 2024 ยท 1 minute read
A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations:

  • m + t = 38
  • 5m + 2t = 100
  • Rearrange (1) to solve for m - subtract t from each side:
    3. m = 38 - t

    Now, substitute (3) into (2)
    5(38 - t) + 2t = 100
    190 - 5t + 2t = 100

    Combine like terms:
    190 - 3t = 100

    Using our equation solver, we get t = 30.

    Plugging t = 30 into (1), we get:
    30 + t = 38

    Using our equation solver again, we get m = 8.

    Check our work for (1)
    8 + 30 = 38 <-- Check

    Check our work for (2)
    5(8) + 2(30) ? 100
    40 + 60 ? 100
    100 = 100 <-- Check

    You could also use our simultaneous equations calculator

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