Scoring in Golf. A golfer played 8 rounds on a tournament
course with the following scores (par is the expected score for a round; negative numbers represent the number of strokes under par for the round,
and positive numbers represent the number of strokes over par for the round): +5, -2, +3, -1, -3, +6, +2, -7
The golfer played 2 more rounds, ending with an even par total for the 10 rounds. Her score for the last round was 7 more than her score on the next-to-last round. What scores did the golfer have on the last two rounds?
To solve this problem, we need to analyze the given information step by step.
First, let's calculate the total score for the first 8 rounds:
Total = +5 - 2 + 3 - 1 - 3 + 6 + 2 - 7
= 3
Next, let's determine the total score for all 10 rounds:
Even par means the golfer's score is equal to par, so the total score for all 10 rounds should be zero. Therefore, we can write an equation to represent this:
Total + Score of the 9th round + Score of the 10th round = 0
Since we already know the value of the Total, we can simplify the equation:
3 + Score of the 9th round + Score of the 10th round = 0
Score of the 9th round + Score of the 10th round = -3
Lastly, we are given another piece of information that the score for the last round was 7 more than the score of the next-to-last round. Let's represent these scores with variables:
Score of the 10th round = x
Score of the 9th round = x - 7
Substituting these values into the equation:
(x - 7) + x = -3
Combining like terms:
2x - 7 = -3
Adding 7 to both sides:
2x = 4
Dividing by 2:
x = 2
Now we know the score of the 10th round is 2, and the score of the 9th round can be found using the equation:
Score of the 9th round = 2 - 7 = -5
Therefore, the golfer had a score of -5 on the 9th round and a score of 2 on the 10th round.