half of a certain number added to its one third gives 15. find the number

Dear Student,
Let the number be x.
Then half of the number will be $\frac{x}{2}$ and one third of the number will be $\frac{x}{3}$
When we add both we get 15. So,
$$\begin{gathered} \frac{x}{2}+\frac{x}{3}=15 \\ LCM of 2 and 3 is 6 \\ \frac{{\displaystyle x}}{{\displaystyle 2}}\times \frac{3}{3}+\frac{{\displaystyle x}}{{\displaystyle 3}}\times \frac{2}{2}=15 \\ \frac{3x+2x}{6}=15 \\ 3x+2x=15\times 6 \\ 5x=90 \\ x=\frac{90}{5} \\ x=18 \end{gathered}$$

The required number is 18

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