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The amount of blood in a person's body varies directly with body weight. A person who weighs 160 lb has about 4.6 qt of blood. About how many quarts of blood are in the body of a 175-lb person?

-How can you find the constant of variation?

-Can you write an equation that relates quarts of blood to weight?

-How can you use the equation to determine solution?

Verified Answer :

pingwin09

The statements expresses as
w ∝ b
where w = body's weight, b = amount of blood

Changing it into a direct variation becomes
w = kb    or   k = w/b
where k = proportionality constant

We know that k is obviously constant, we equation it into two states as
w₁/b₁ = w₂/b₂

Given that w₁ = 160 lb, b₁ = 4.6 qt, b₂ = 175, w₂ = 175 lb. Then b₂ will be
160/4.6 = 175/b₂
b₂ = 160/(4.6*175) = 160/805 = 0.20 quarts

Your questions are integrated in just step-by-step solution. 

Step-by-step explanation:

Given that amount of blood is directly linked to body weight of the person.

\(b\propto W\)

\(b=kW\)

\(\frac{b}{W}=k\)

b = Amount of blood

W = weight of the person

k = proportionality constant or constant of variation

1) Given that, person who weighs 160 lb has about 4.6 quart of blood.

b = 4.6 quart, W = 160 lb

\(k=\frac{b}{W}=\frac{4.6 quart}{160 lb}=0.02875 quart/lb\)

The constant of variation is of value 0.02875 quart/lb.

2) An equation that relates quarts of blood to weight:

\(b=0.02875 quart/lb\times W\)

3) If, b = ?,W = 175 lb

\(b=0.02875 quart/lb\times W\)

\(b=0.02875 quart/lb\times 175 lb=5.03125 quart\)

5.03125 quarts of blood are in the body of a 175-lb person.

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