a. The absolute value equation that can be used to determine the least number of runners is |X - m| = 110
b. The least number of runners in a race was 730 runners.
The question has to do with absolute value of a number
<h3>What is the absolute value of a number?</h3>
The absolute value of a number or modulus is the magnitude of that number.
<h3>What absolute value equation can be written to determine the least number of runners?</h3>
Given that the average number of runners for the past two years is 840 and the maximum number of runner is 950.
Let
- X = average number of runners = 840
- M = maximum number of runner = 950 and
- m = least number of runners
Since the difference between the average number of runners and the greatest number of runners is the same as the difference between the average number of runners and the least number of runners.
We have that |X - M| = |X - m|
|840 - 950| = |X - m|
|X - m| = |-110|
|X - m| = 110
So, the absolute value equation that can be used to determine the least number of runners is |X - m| = 110
<h3>b. What is this value of least number of runners?</h3>
Since |X - m| = 110
Substituting X = 840 into the equation, we have
840 - m = 110
m = 840 - 110
m = 730
So, the least number of runners in a race was 730 runners.
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