Write the integer that is represented by a point midway between -76 and 76 on the number line.
Choose a nonzero integer for n to show that –n can be evaluated as a positive number.
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?
zero;
n=-9
Sum of first 8 rounds: +3.
sum of first 10 rounds: 0
so sum of last two is +3, or 3=7+n so n has to be -4
To find the integer that is represented by a point midway between -76 and 76 on the number line, you can calculate the average of -76 and 76.
To do this, you add -76 and 76 together and divide the sum by 2:
(-76 + 76) / 2 = 0 / 2 = 0.
Therefore, the integer represented by a point midway between -76 and 76 is 0.
To show that -n can be evaluated as a positive number, you can choose a nonzero integer for n and evaluate -n.
For example, let's choose n = 5. Evaluating -5, we get:
-n = -5 = 5.
Therefore, when you evaluate -n, you get a positive number. This holds true for any nonzero integer you choose.
For the golf scoring problem, let's work through it step by step.
We know that the golfer played 8 rounds with scores: +5, -2, +3, -1, -3, +6, +2, -7.
The par total for these 8 rounds can be calculated by summing up the scores:
+5 + (-2) + 3 + (-1) + (-3) + 6 + 2 + (-7) = +3.
To have an even par total after playing 10 rounds, we need the last two rounds to cancel out the +3 par total of the first 8 rounds.
Let's represent the scores for the last two rounds as x and x+7 (since the score for the last round is 7 more than the score for the next-to-last round).
Adding the scores for the last two rounds to the par total, we get:
+3 + x + (x + 7) = 0.
Simplifying this equation, we have:
2x + 10 = 0.
To solve for x, we subtract 10 from both sides:
2x = -10.
Finally, we divide both sides by 2 to find the value of x:
x = -5.
Therefore, the scores for the last two rounds are -5 and (-5 + 7), which simplifies to -5 and +2.