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

Scores are Joe = 78

Tom = 85

Nick = 68

Step-by-step 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