An exam worth 269 points contains 36 questions. Some questions are worth 7 points, and the others are worth 8 points. How many 7 point and 8 point questions are on the test?

Answer:There are 19 questions worth 7 points.There are 17 questions worth 8 points.Step-by-step explanation:Assign variables:Let x = number of questions worth 7 points.Let y = number of questions worth 8 points.First we deal with the number of questions.There are 36 questions, so our first equation is:x + y = 36Now we deal with the points.x questions worth 7 points each are worth 7x points.y questions worth 8 points each are worth 8y points.The total worth of all the questions is 7x + 8y.The total worth of the exam is 269, so our second equation is7x + 8y = 269We have a system of 2 equations in 2 variables.x + y = 367x + 8y = 269Let's use the substitution method to solve the system of equations.Solve the first equation for x.x + y = 36x = 36 - ySubstitute 36 - y in for x in the second equation.7x + 8y = 2697(36 - y) + 8y = 269Distribute the 7.252 - 7y + 8y = 269Combine like terms.252 + y = 269Subtract 252 from both sides.y = 17There are 17 questions worth 8 points.x + y = 36x + 17 = 36x = 19There are 19 questions worth 7 points.Check:What does 19 questions at 7 points each and 17 questions at 8 points each add to?19 * 7 + 17 * 8 = 133 + 136 = 269The points add to 269, so our answer is correct.