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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

Blood volume, $V sub B$ , in a human can be determined using the equation $V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction$ , where $V sub P$ is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

ExplanationShow

Choice A is correct. The hematocrit can be expressed in terms of the blood volume and the plasma volume by solving the given equation $V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction$ for H. Multiplying both sides of this equation by $open parenthesis, 1 minus H, close parenthesis$ yields $V sub B, times, open parenthesis, 1 minus H, close parenthesis, equals V sub P$ . Dividing both sides by $V sub B$ yields $1 minus H equals, the fraction V sub P, over V sub B$ . Subtracting 1 from both sides yields $negative H equals, negative 1 plus, the fraction V sub P over V sub B$ . Dividing both sides by $negative 1$ yields $H equals, 1 minus, the fraction V sub P over V sub B$ .

Choices B, C, and D are incorrect and may result from errors made when manipulating the equation.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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