Answer:
The number is 12
Explanation:
Let the number = n
[tex]\begin{gathered} \text{ One-half of the number}=\frac{1}{2}n \\ 2\text{ more than one-third of the number}=2+\frac{1}{3}n \end{gathered}[/tex]Thus, the given statement written as a mathematical equation is:
[tex]\frac{1}{2}n=\frac{1}{3}n+2[/tex]We solve the equation for the number, n.
[tex]\begin{gathered} \frac{n}{2}=\frac{n}{3}+2 \\ \text{The lowest common multiple of the denominators, }2\text{ and 3}=6 \\ \text{Multiply all through by }6 \\ \frac{6n}{2}=\frac{6n}{3}+2(6) \\ 3n=2n+12 \\ \text{ Subtract 2n from both sides of the equation.} \\ 3n-2n=2n-2n+12 \\ n=12 \end{gathered}[/tex]The number is 12.
