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.
Solve the two equations simultaneously: 3x+5y=100 x+y=24 Multiply the 2nd equation by 3 so you can have the same coefficient of one of the variables (in this case, x) 3x+5y=100 3x+3y=72 Minus the second equation from the first to give you: 2y=28 Divide by 2 on both sides to give you y=14 Substitute 14 for y into one of the equations: x+y=24 x=10 Remember that 3x+5y=100 So the test contains 10 3 point questions and 14 5 point questions.
