Question

Joe, Tom, and Nick play a round of golf together. Their combined score is 231. Joe’s score was 10 more than Nick’s score, and Tom’s score was 7 more than Joes score . What was each persons score? Solve using a system of three equations and using elimination.

Answer 1

Answer:

    Scores are    Joe = 78

                           Tom = 85

                            Nick = 68

Explanation:

Let us take Joe, Tom and Nick's score as a, b,c respectively.

We have combined score = 231

   a + b + c = 231   ----------------------------------Equation 1

 Joe’s score was 10 more than Nick’s score

    a = c + 10

    a - c = 10   ----------------------------------Equation 2

 Tom’s score was 7 more than Joe's score

    b = a + 7

    b - a = 7   ----------------------------------Equation 3

Equation 1 + Equation 2 gives

      a + b + c + a - c = 231 + 10

      2a + b = 241   ----------------------------------Equation 4

Equation 4 - Equation 3 gives

       2a + b -( b - a) = 241 - 7

        3a = 234

           a = 78

Substituting in equation 3 and equation 2,

     b - 78 = 7

          b = 85

     78 - c = 10

          c = 68

So scores are    Joe = 78

                           Tom = 85

                           Nick = 68