Question

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.

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

Answer 1

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

(Here x is number of 5-point questions and y is number of 2-point questions. If you solve: y = 29 − x, 5x + 2(29 − x) = 100 ⇒ 3x = 42 ⇒ x = 14, y = 15.)