Question 1170438: Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. Create a system that would determine how many of each question type is on the test.
Answer by math_tutor2020(3817)   (Show Source):
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x = number of multiple choice questions
y = number of open-ended questions
Since there are 38 questions of either type, this means x+y = 38 is the first equation.
Each multiple choice question is worth 4 points. If a student answers all x of them correctly, then they earn 4x points.
Each open-ended question is worth 20 points. If they answer all y of them correctly, then they earn 20y points.
In total, there are 4x+20y points which is set equal to 200, since this is the total number of points possible on the exam.
The second equation is therefore 4x+20y = 200
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In summary, the system of equations is
x+y = 38
4x+20y = 200
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