Word problem

Question

12 problems on a math test. Five points were given for each correct answer, and two points were deducted for each incorrect answer. His score was 39, how many correct answers did he have?

Answer 1

First, understand the problem.

 

Then, assign variables.  If possible, assign a variable to the value the problem asks you to find.  So, let:

   x = number of correct answers

 

Then, translate the words (phrases) into math expressions (variables and operations):

  "12 problems on a math test"  means  that  number of incorrect answers is  12-x

  "Five points were given for each correct answer"   means    +5x

  "two points were deducted for each incorrect answer"    means    -2(12-x)

  "His score was 39"    means    5x - 2(12-x) = 39

  "how many correct answers did he have?"    means    report x

 

Now, the easy math:

   5x -2(12-x)=39

    7x - 24 = 39

      7x = 63

        x=9

 

Checking (very important):

  Is 5(9) - 2(12-5) = 39   ?

       45 - 6 = 39   ?

          39 = 39   ?  yes

Answer 2

Let x = number of questions correct.

 

Then, 12 - x = number of incorrect answers

 

So, 5x - 2(12-x) = 39

 

     5x - 24 + 2x = 39

 

                   7x = 63

 

                    x = 9

 

He got 9 questions right and 3 questions wrong.