Question

One half of a number is 2 more than one third of the number . find the number

Answer 1

The number is 12

Explanation:

Let the number = n

`\begin{gathered} \text{ One-half of the number}=(1)/(2)n \\ 2\text{ more than one-third of the number}=2+(1)/(3)n \end{gathered}`

Thus, the given statement written as a mathematical equation is:

`(1)/(2)n=(1)/(3)n+2`

We solve the equation for the number, n.

`\begin{gathered} (n)/(2)=(n)/(3)+2 \\ \text{The lowest common multiple of the denominators, }2\text{ and 3}=6 \\ \text{Multiply all through by }6 \\ (6n)/(2)=(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}`

The number is 12.