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On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions are on the test?

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  1. a = 2 pt, b = 4 pt, c = 5 pt

    a + b + c = 28

    2a + 4b + 5c = 100

    a = 2c

    2a + 2b + 2c = 56
    ... substituting ... 3a + 2b = 56

    4a + 8b + 10c = 200
    ... substituting ... 9a + 8b = 200

    subtract the equations (after multiplying) to eliminate b

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