Question

Mr. Martin’s math test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points.

Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.

x + y = 29, 5x + 2y = 100

How many problems of each point value are on the test?

10 problems worth 5 points and 25 problems worth 2 points
14 problems worth 5 points and 15 problems worth 2 points
16 problems worth 5 points and 13 problems worth 2 points
15 problems worth 5 points and 13 problems worth 2 points

Answer 1

x + y = 29 and 5x + 2y = 100. From the first, y = 29 − x. Substitute: 5x + 2(29 − x) = 100 → 3x = 42 → x = 14, so y = 15.

Answer: 14 problems worth 5 points and 15 problems worth 2 points.