B.5 Additive property of length 7RA
$R$ is a point on segment $\overline{Q S}$. If $Q R=8 x, R S=x+10$, and $Q S=5 x+18$, what is $Q R$ ?
Simplify your answer and write it as a proper fraction, mixed number, or integer.
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Answer

$\boxed{16}$ is the final answer.

Steps

Step 1 ：The problem is asking for the length of segment QR. We know that QR + RS = QS due to the additive property of length.

Step 2 ：We can set up an equation using the given lengths: $8x + x + 10 = 5x + 18$.

Step 3 ：Solving this equation gives us the value of x as 2.

Step 4 ：Substituting x = 2 back into the expression for QR gives us $QR = 8x = 16$.

Step 5 ：$\boxed{16}$ is the final answer.