The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $10$.  Find the sum of the $x$-coordinates of the midpoints of the sides of the triangle.
Question:
The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $10$.  Find the sum of the $x$-coordinates of the midpoints of the sides of the triangle.
Answer:
Let's think step by step.

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The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $10$.  Find the sum of the $x$-coordinates of the midpoints of the sides of the triangle.
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