Question

Half of a certain number added to its one - third gives 15. Find the number

Answer 1

Basically we need to setup an equation that models the situation and solve it.
Let $x=\text{the required number}$

Half of $x$ is  $\dfrac{x}{2}$ and one third of  $x$ is  $\dfrac{x}{3}$.
Add up and set them equal to $15$ :
$\dfrac{x}{2}+\dfrac{x}{3}=15$
write the fractions using a common denominator $6$ :
$\dfrac{3x}{6}+\dfrac{2x}{6}=15$
combine like terms :
$\dfrac{5x}{6}=15$
multiply each side by $\dfrac{6}{5}$, the reciprocal of  $\dfrac{5}{6}$ :
$\dfrac{6}{5}\left(\dfrac{5x}{6}\right)=\dfrac{6}{5}\left(15\right)$
simplify :
$x=18$

Answer 2

Let the number be  X.
half of the number = X / 2
one third of the number = X / 3

$\frac{X}{2}+\frac{X}{3}=15\\\\\frac{3*X+2*X}{6}=15\\\\\frac{5X}{6}=15=3 * 5\\\\X=3*5*\frac{6}{5}=18$

so the number is 18.
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verify again:      half of 18 = 9  
               one third of 18  = 6
     add them to get 15.      so it verifies  ok.