Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?

Let x be the number of 4-point problems and y the number of 3-point problems. Since there are 40 problems, x + y = 40; the total score is 4x + 3y = 130. If all 40 problems were worth 3 points, they would total 120 points, so the extra 10 points mean 10 problems were worth 4 points. That leaves 30 problems worth 3 points, matching choice B.

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