A biology test is worth 100 points and has 36 questions.
a. Multiple-choice questions are worth 2 points each and essay questions are worth 6 points each. How many questions of each type are on the test?
b. Your friend says that it is possible for the multiple-choice questions to be worth 4 points each. Is your friend correct? Explain.
a. Let the number of 2 pt questions = N
So the number of pt questions =36 - N
So we have that
2N + 6 (36 - N) = 100 simplify
2N + 216 - 6N = 100
-4N + 216 =100
-4N = -116 divide both sides by -4
N = 29 = 2 pt questions
36 - 29 = 7 = 6 pt questions