Sarah received a score of 36 points on an exam. The exam consisted of multiple choice questions that were worth 3 points for a correct answer and free response questions that were worth 5 points for a correct answer. If she answered a total of 10 questions correctly, how many of each type of question did she get correct?

Sarah answered 7 multiple choice questions and 3 free response questions correctly.

Step-by-step explanation:

Given that: she has 36 points.

                   3 points each for the multiple choice question (MCQ)

                   5 points each for the free response question (FRQ)

To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.

  3x + 5y = 36   1

Since she answered a total of 10 question, then;

  x + y = 10

 x = 10 - y    2

Substitute equation 2 into 1,

3(10 - y) + 5y = 36

30 - 3y + 5y = 36

2y = 6

y = 3

Substitute the value of y in equation 2,

x = 10 - y

  = 10 - 3

  = 7

x = 7, y = 3

Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.