Answer
48
Work Step by Step
Let the unknown number be $x$. Three-eight of this number is $\frac{3}{8}x$ while five-sixth of this number is $\frac{5}{6}x$. Since when three-eighths of a number is subtracted from five-sixths of the number, the result is 22, we write the following equation and solve:
$\frac{5}{6}x-\frac{3}{8}x=22$
$\frac{5x}{6}-\frac{3x}{8}=22$
$\frac{5x(4)-3(3x)}{24}=22$
$\frac{20x-9x}{24}=22$
$\frac{11x}{24}=22$
$11x=528$
$x=\frac{528}{11}=48$
Therefore, the unknown number is 48.
