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? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answer 1

1. There are x 3-point questions, and y 5-point questions.

In total there are 24 questions mean : x+y=24,
In total there are 100 points, so x*3 (x questions each 3 points of worth)+y*5 (y questions each 5 point of worth) make a total of 100 points.

The situation is described by the system:
(i) x+y=24
(ii) 3x+5y=100

from x+y=24, we can write y=24-x
substitute in (ii):

3x+5(24-x)=100
3x+5*24-5*x=100
3x+120-5x=100
3x-5x=100-120
-2x=-20

x=-20/(-2)=10

from this, y=24-x=24-10=12

Answer: The test contains 10 three-point questions and 14 five-point questions.