Question

E is the midpoint of BC. If BE = 50 and CE = 2x + 25, find the value of x.

Answer 1

Answer:

The value of $x$ is $\frac{25}{2}$.

Step-by-step explanation:

From Analytical Geometry we get that ratio of BC to BE is:

$\frac{BC}{BE} = 2$ (From definition of midpoint)

$\frac{BE+CE}{BE} = 2$

$1 + \frac{CE}{BE} = 2$

$\frac{CE}{BE} = 1$

$CE = BE$

If we know that $BE = 50$ and $CE = 2\cdot x + 25$, then, the equality above is expanded:

$2\cdot x +25 = 50$

$2\cdot x = 25$

$x = \frac{25}{2}$

The value of $x$ is $\frac{25}{2}$.