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The ages of three brothers are consecutive integers with the sum of 96.

Let $x$be the first integer representing the age of a brother.

Then, the three consecutive integers representing the ages of the brothers are $x$, $x+1$and $x+2$.

Translating the given problem into equation form,

$x+x+1+x+2=96$

This is the required equation for the given problem.

Solving,

$x+x+1+x+2=96$ (Obtained equation)

$3x+3=96$ (Simplify)

$3x+3鈭�3=96鈭�3$ (Subtract 3 from both sides)

$3x=93$ (Simplify)

$\frac{3x}{3}=\frac{93}{3}$ (Divide both sides by 3)

$x=31$ (Simplify)

So, $x=31$is the solution of the obtained equation.

According to the assumption, $x$is the first of the three consecutive integers which represents the ages of the brothers in the given problem.

Thus, the ages of the three brothers, in order are 31, 32 and 33.