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Objectives

? Perform operations with radical expressions.
? Determine the number of solutions for a quadratic equation by using the discriminant.
? Solve word problems using quadratic equations.

#### Solution Preview

Commuting students. At a well-known university, 1/4of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students drive more than 40 miles daily, and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles daily?

Let the number of graduate students be 150. Then the number of undergraduate students is 300. Fraction of the graduate students who commute = (1/3)(150) = 50 and fraction of the undergraduate students who commute = (1/4)(300) = 75
 Total commuters = 50 + 75 = 125
Graduate students who drive more than 40 miles daily = (1/6)(50) = 25/3 and undergraduate students who drive more than 40 miles daily = ...

#### Solution Summary

Radical expressions, equations and quadratic formulas are determined. A complete, neat and step-by-step solution is provided in the attached file.

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