A mother dolphin is 150.25 meters below sea level, and her calf is 45 meters below sea level. Use absolute values to determine which dolphin is farthest from the surface and explai... A mother dolphin is 150.25 meters below sea level, and her calf is 45 meters below sea level. Use absolute values to determine which dolphin is farthest from the surface and explain your reasoning.

Understand the Problem

The question asks us to determine which of the two dolphins (mother and calf) is farthest from the surface of the water using absolute values. The position of each dolphin is given as a depth below sea level, and we need to use absolute values to represent these depths as distances from the surface. Then, we compare the distances to determine which dolphin is farther.

Answer

The mother dolphin is farther from the surface.
Answer for screen readers

The mother dolphin is farther from the surface.

Steps to Solve

  1. Find the absolute value of the mother dolphin's position

The mother dolphin is at $-25$ feet. The absolute value represents the distance from the surface.

$|-25| = 25$ feet

  1. Find the absolute value of the calf dolphin's position

The calf is at $-17$ feet. The absolute value represents the distance from the surface.

$|-17| = 17$ feet

  1. Compare the distances

Compare the absolute values to see which dolphin is farther from the surface.

Since $25 > 17$, the mother dolphin is farther from the surface.

The mother dolphin is farther from the surface.

More Information

Absolute value is used to represent the magnitude (distance) of a number from zero, irrespective of its sign. In this scenario, it helps us consider the depth of the dolphins as a positive distance from the surface of the water.

Tips

A common mistake is to simply compare the numbers $-25$ and $-17$ without taking the absolute value. This would incorrectly lead to the conclusion that the calf is farther from the surface because $-17 > -25$. Remember, we're interested in the distance from the surface, not the numerical value of the depth.

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