Let $w,$ $x,$ $y,$ and $z$ be nonnegative numbers whose sum is 100.  Find the largest possible value of
\[wx + xy + yz.\]
Question:
Let $w,$ $x,$ $y,$ and $z$ be nonnegative numbers whose sum is 100.  Find the largest possible value of
\[wx + xy + yz.\]
Answer:
Let's think step by step.

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Let $w,$ $x,$ $y,$ and $z$ be nonnegative numbers whose sum is 100.  Find the largest possible value of
\[wx + xy + yz.\]
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