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......multiply by -2
5x + 2y = 100
-----------------
-2x - 2y = - 58 (result of multiplying by -2)
5x + 2y = 100
----------------add
3x = 42
x = 42/3
x = 14 <==== there were 14 five-point questions

x + y = 29
14 + y = 29
y = 29 - 14
y = 15 <=== there were 15 two-point questions