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?
Answers
Step-by-step explanation:
Given that amount of blood is directly linked to body weight of the person.
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
The constant of variation is of value 0.02875 quart/lb.
2) An equation that relates quarts of blood to weight:
3) If, b = ?,W = 175 lb
5.03125 quarts of blood are in the body of a 175-lb person.
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.
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