03 - Excess of the Sum of Parts over the Difference of Parts of a Number

Let x = the number
x/2 = the half part of x
x/3 = the third part of x
x/4 = the fourth part of x
x/5 = the fifth part of x
 

S₁ = sum of the half and third parts
$S_1 = \dfrac{x}{2} + \dfrac{x}{3}$
 

S₂ = difference of fourth and fifth parts
$S_2 = \dfrac{x}{4} - \dfrac{x}{5}$
 

The excess of S₁ over S₂ = 188
$S_1 - S_2 = 188$

$\left( \dfrac{x}{2} + \dfrac{x}{3} \right) - \left( \dfrac{x}{4} - \dfrac{x}{5} \right) = 188$

$\frac{47}{60}x = 188$

$x = 240$       answer