ANSWER
[tex]b =11 \frac{2}{3} [/tex]
EXPLANATION
The given function is
[tex]f(x) = \frac{200}{x - b} [/tex]
It was given that
[tex]f(13) = 150[/tex]
This implies that,
[tex]150 = \frac{200}{13- b} [/tex]
Cross multiply to get:
[tex]150(13 - b) = 200[/tex]
[tex]1950 - 150b = 200[/tex]
[tex] - 150b = 200 - 1950[/tex]
[tex] - 150b = - 1750[/tex]
Divide both sides by -150.
[tex]b = \frac{ - 1750}{ - 150} [/tex]
[tex]b = \frac{ 35}{3} [/tex]
[tex]b =11 \frac{2}{3} [/tex]
