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.
Remark. The easiest way to solve this is to make the coefficients of one of the letters = to the same coefficient in the other equation
Set up and solve x + y = 24 3x + 5y = 100 Multiply the first equation by 3 <u>3x + 3y = 72 </u> Subtract 2y = 28 Divide by 2 y = 28/2 y = 14 <<<<<< Answer for y
Step 2 Solve for x x + y = 24 x + 14 = 24 Subtract 14 from both sides. x = 24 - 14 x = 10 <<<<Answer for x
