Solution to Problem 231


A correct solution came from Bradley student Lena Folwaczny.
Other correct solutions were submitted by Bill Webb, Nancy Schwarzkopf, Aaron Kahn, Juan Carlos Marivela, A. Teitelman, Al Zimmermann, Ron Welch and Bryan Fluhrer.


The fraction (a + c) / (b + d) will always be between a / b and c / d.

Since a / b < c / d, a d < b c.
This means that a (b + d) = a b + a d < a b + b c = b (a + c), so a / b < (a + c) / (b + d).
It also means that (a + c) d = a d + c d < b c + c d = (b + d) c, so (a + c) / (b + d) < c / d.

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