Chapter 5.2, Problem 34PPE

a.

To determine

To determine the constant of variation.

Answer to Problem 34PPE

  $k=34.76$

Explanation of Solution

Given:

Blood in a person’s body varies directly with the body weight

Person weight 160 lb has 4.6 quarts of blood

Concept used:

Basic algebraic equations

Calculation:

Let’s consider the equation as,

  $\Rightarrow y=kx$

Where, $y=160\text{lb}$ and $x=4.6$ quarts of blood

Substituting the values of $x$ and $y$ ,

  $\Rightarrow 160=k\times 4.6$

  $\Rightarrow \frac{160}{4.6}=k$

  $\Rightarrow k=34.76$

Conclusion:

Therefore, the constant of variation is $k=\mathrm{34.76.}$

b.

To determine

To determine the equation that relates quarts of blood to weight.

Answer to Problem 34PPE

  $y=34.76\times x$

Explanation of Solution

Given:

Blood in a person’s body varies directly with the body weight

Person weight 160 lb has 4.6 quarts of blood

Concept used:

Basic algebraic equations

Calculation:

Let’s consider the equation as,

  $\Rightarrow y=kx$

Where, $y=160\text{lb}$ and $x=4.6$ quarts of blood

Substituting the values of $x$ and $y$ ,

  $\Rightarrow 160=k\times 4.6$

  $\Rightarrow \frac{160}{4.6}=k$

  $\Rightarrow k=34.76$

So,

  $\Rightarrow y=kx$

  $\Rightarrow y=34.76\times x$

Conclusion:

Therefore, the equation that relates quarts of blood to weight is $y=34.76\times x.$

c.

To determine

To determine the solution from the equation.

Answer to Problem 34PPE

  $x=5.034$

Explanation of Solution

Given:

Blood in a person’s body varies directly with the body weight

Person weight 160 lb has 4.6 quarts of blood

Person weight 175 lb

Concept used:

Basic algebraic equations

Calculation:

Let’s consider the equation as,

  $\Rightarrow y=kx$

Where, $y=160\text{lb}$ and $x=4.6$ quarts of blood

Substituting the values of $x$ and $y$ ,

  $\Rightarrow 160=k\times 4.6$

  $\Rightarrow \frac{160}{4.6}=k$

  $\Rightarrow k=34.76$

So,

  $\Rightarrow y=kx$

  $\Rightarrow y=34.76\times x$

Now, when the value of $y=175$ ,

Value of $x$ is,

Putting the value $x$ in equation (i),

  $\Rightarrow 175=34.76\times x$

  $\Rightarrow \frac{175}{34.76}=x$

  $\Rightarrow x=5.034$

Conclusion:

Therefore, the solution from the equation is $x=5.034$ or $5.034$ quarts of blood.