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Chapter 6: Problem 109

The volume of blood in a person's body is proportional to body weight. A person who weighs 160 pounds has approximately 5 quarts of blood. Estimate the number of quarts of blood in a person who weighs 200 pounds.

Short Answer

Expert verified
The volume of blood in a person who weighs 200 pounds is approximately 6.25 quarts.

Step by step solution

01

Understand the given relationship

The problem states that a person who weighs 160 pounds has approximately 5 quarts of blood. This means that 160 pounds corresponds to 5 quarts of blood, establishing a proportion between weight and blood volume.
02

Set up the proportion

The goal is to estimate the number of quarts of blood in a person who weighs 200 pounds. Set up a proportion as follows: \(\frac{{160 \, \text{{pounds}}}}{{5 \, \text{{quarts}}}} = \frac{{200 \, \text{{pounds}}}}{{x \, \text{{quarts}}}}\), where \(x\) represents the volume of blood for a 200-pound person.
03

Solve the proportion

Cross-multiply to solve for \(x\). This gives: \(160 * x = 200 * 5\). Solving for \(x\) yields \(x = \frac{{200 * 5}}{{160}}\).

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