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.

    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

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step-by-step explanation: