[tex]\displaystyle \\
\text{We use the following equation:} \\ \\
\frac{n}{2} = n - 38 \\ \\
We solve for n: \\ \\
\frac{n}{2} = n - 38 ~~\Big| \times 2 \\ \\
n = 2 \times n - 2 \times 38 \\ \\
n = 2n - 76 \\ \\
2n - n = 76 \\ \\
\boxed{n = 76} \\ \\
\text{Verification: } \\ \\
\frac{n}{2} = n - 38 \\ \\
\frac{76}{2} = 76 - 38 \\ \\
\boxed{38 = 38 ~~~ Correct } [/tex]
