Problema Solution
A student took 60 minutes to answer a combination of 20 multiple choice and extended response questions. She took 2 minutes to answer each multiple choice question and 6 minutes to answer each extended response question.
Write a system of equations to model the relationship between the number of multiple choice question m and the number of extended response questions r
How many of each type of question was on the test
Answer provided by our tutors
m = the number of multiple choice question
r = the number of extended response questions
the total number of questions is 20
m + r = 20
it took total of 60 minutes to answer the questions
2 min per question for m questions + 6 minutes per question for r questions = total of 60 minutes
2m + 6r = 60
we have the following system of equations
m + r = 20
2m + 6r = 60
by solving the system we find
m = 15 multiple choice question
r = 5 extended response questions
there were 15 multiple choice question and 5 extended response questions on the test.