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A city advertises that the average number of runners over the past two decades in their annual road race is 840.

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. The greatest number of runners in a race was 950.

What absolute value equation can be written to determine the least number of runners, and what is this value?

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Absolute value equation: l x- l =

The least number of runners in a race was

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oladayoademosu

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

What is the absolute value of a number?

The absolute value of a number or modulus is the magnitude of that number.

What absolute value equation can be written to determine the least number of runners?

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

b. What is this value of least number of runners?

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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