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

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

D equals, T minus, the fraction 9 over 25, end fraction, times open parenthesis, 100 minus H, close parenthesis

The formula above can be used to approximate the dew point D, in degrees Fahrenheit, given the temperature T, in degrees Fahrenheit, and the relative humidity of H percent, where H is greater than 50. Which of the following expresses the relative humidity in terms of the temperature and the dew point?

ExplanationShow

Choice A is correct. It’s given that D equals, T minus the fraction 9 over 25, end fraction, times, open parenthesis, 100 minus H, close parenthesis. Solving this formula for H expresses the relative humidity in terms of the temperature and the dew point. Subtracting T from both sides of this equation yields D minus T equals, the negative of the fraction 9 over 25, end fraction, times, open parenthesis, 100 minus H, close parenthesis. Multiplying both sides by the negative of the fraction 25 over 9 yields the negative of the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, equals, 100 minus H. Subtracting 100 from both sides yields the negative of the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, minus 100, equals negative H. Multiplying both sides by negative 1 results in the formula the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, plus 100, equals H..

Choices B, C, and D are incorrect and may result from errors made when rewriting the given formula.

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