multiple choice: 2 pointsshort response: 4 pointsStep-by-step explanation:
I often find the difficult part of "this situation" questions to be determining exactly what "situation" is of interest.
You have to read ahead to the last part of the question to determine that the point values of the questions are unknown, and you are supposed to find them based on the given numbers of right questions and total scores.
You know from your experience with tests and scoring that the total score is the sum of the scores for each question type; and that each question type is scored based on the number of right answers and the point value of each.
(a) If we let m and s represent the point values of multple-choice and short-response questions, respectively, then the table and problem wording tell us ...
... 23m +10s = 86 . . . . . your score
... 28m +5s = 76 . . . . . . your friend's score
This is your system of linear equations.
(b) The equations can be solved numerous ways. One way is to subtract the first equation from 2 times the second equation. This will eliminate the variable s.
... 2(28m +5s) -(23m +10s) = 2(76) -(86)
... 33m = 66 . . . . . simplify
... 66/33 = m = 2 . . . . divide by 33
Now, we can substitute this value into the first equation to find s.
... 23·2 +10s = 86
... 10s = 40 . . . . . . . . . subtract 46
... 40/10 = s = 4 . . . . . divide by 10
Multiple-choice questions are worth 2 points; short-response questions are worth 4 points.
