Math  /  Algebra

Question19. BIOLOGY The number of pints of blood in a human body varies directly with the person's weight. A person who weighs 120 pounds has about 8.4 pints of blood in his or her body. a. Write and graph an equation relating weight and amount of blood in a person's body. b. Predict the weight of a person whose body holds 12 pints of blood.

Studdy Solution

STEP 1

1. The number of pints of blood varies directly with the person's weight.
2. A person weighing 120 pounds has 8.4 pints of blood.
3. We need to find an equation relating weight and blood volume.
4. We need to predict the weight of a person with 12 pints of blood.

STEP 2

1. Define the relationship and write the equation.
2. Graph the equation.
3. Use the equation to predict the weight for 12 pints of blood.

STEP 3

Define the relationship and write the equation.
Since the number of pints of blood varies directly with weight, we can express this relationship as:
B=kW B = kW
where B B is the number of pints of blood, W W is the weight in pounds, and k k is the constant of proportionality.
Given that when W=120 W = 120 , B=8.4 B = 8.4 , we can find k k by substituting these values into the equation:
8.4=k×120 8.4 = k \times 120
Solve for k k :
k=8.4120 k = \frac{8.4}{120} k=0.07 k = 0.07
Thus, the equation relating weight and blood volume is:
B=0.07W B = 0.07W

STEP 4

Graph the equation.
To graph the equation B=0.07W B = 0.07W , plot the weight W W on the x-axis and the blood volume B B on the y-axis. Use the equation to calculate points:
- When W=0 W = 0 , B=0.07×0=0 B = 0.07 \times 0 = 0 - When W=120 W = 120 , B=0.07×120=8.4 B = 0.07 \times 120 = 8.4
Draw a straight line through these points, as the relationship is linear.

STEP 5

Use the equation to predict the weight for 12 pints of blood.
Substitute B=12 B = 12 into the equation B=0.07W B = 0.07W :
12=0.07W 12 = 0.07W
Solve for W W :
W=120.07 W = \frac{12}{0.07} W=171.43 W = 171.43
Thus, the predicted weight of a person whose body holds 12 pints of blood is approximately:
171.43 \boxed{171.43} pounds

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