Can someone explain to me how to do this problem? 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? Thanks.
Total for the first 8 rounds
= +5 -2 +3 -1 +6 +2 -7
= +3
Let x=score for last round, the
Total for 10 rounds
= +3 + (x-7) + x
= 0 (par)
2x -7 + 3=0
x=2 (last round)
x=2-7= -5 (last but one round)
Answer 0
To solve this problem, let's work through it step by step.
Step 1: Calculate the total score for the first 8 rounds. Given scores for the first 8 rounds are:
+5, -2, +3, -1, -3, +6, +2, -7
To find the total score, we sum up these scores:
(5) + (-2) + (3) + (-1) + (-3) + (6) + (2) + (-7) = 3
So, the total score for the first 8 rounds is 3.
Step 2: Since the golfer ended with an even par total after playing 10 rounds, we know that the total score for the last two rounds must be -3 (since 3 - 3 = 0).
Step 3: Let's denote the score for the next-to-last round as x. According to the problem statement, the score for the last round is 7 more than the score on the next-to-last round, which means the score for the last round is x + 7.
Step 4: We can set up an equation using the information from step 2 and step 3:
x + (x + 7) = -3
Solving this equation, we get:
2x + 7 = -3
2x = -3 - 7
2x = -10
x = -10/2
x = -5
So, the score for the next-to-last round (8th round) is -5.
Step 5: Now that we know the score for the next-to-last round (-5), we can find the score for the last round:
Score for the last round = x + 7 = -5 + 7 = 2
Therefore, the scores for the last two rounds are -5 and 2.
To summarize:
The score for the penultimate (next-to-last) round is -5, and the score for the last round is 2.