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I. $x^{2} - 31 x + 240 = 0$ ,
II. $y^{2} - 21 y + 108 = 0$ . How are $x$ and $y$ related?

Competition practiceQuadratic Comparison

A $x$ ≤ $y$
B $x > y$
C $x$ ≥ $y$
D $x < y$

Step-by-Step Solution

I:

(x - 15) (x - 16) = 0

, so

x = 15

or 16. II:

(y - 9) (y - 12) = 0

, so

y = 9

or 12. The smallest

x

(15) exceeds the largest

y

(12), so

x > y

.

Answer: B)

x > y

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