To find the value of ( x ), we can set up a proportion:

[
\frac{8}{25} = \frac{7\frac{1}{2}}{x}
]

Let's convert ( 7\frac{1}{2} ) to an improper fraction:

[
7\frac{1}{2} = \frac{15}{2}
]

Now the proportion becomes:

[
\frac{8}{25} = \frac{15}{2x}
]

To solve for ( x ), we can cross multiply:

[
8 \cdot 2x = 15 \cdot 25
]
[
16x = 375
]
[
x = \frac{375}{16}
]
[
x = 23.4375
]

Therefore, the value of ( x ) is ( 23.4375 ).