Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

Answer 1

First we solve system to see what it indicates.

multiply first equation by 3 and subtract it from second.
it will become
3x + 3y = 72

after subtracting from second we get:
2y = 28
y = 14
x = 24 - 14 = 10

We can conclude that there are more 5 points question. there are 10 three point questions and 14 five point questions.