Question

Two thirds of a number exceeds one-half of the number by 3. find the number

Answer 1

First, let us set x for the missing number.

Then, two-thirds of a number: 2/3 x

exceeds one-half of the number 1/2 by 3

So,

`(2)/(3)x-(1)/(2)x=3`

Solve for x:

Multiply both sides by 6:

`\begin{gathered} 6((2)/(3)x-(1)/(2)x)=6\ast3 \\ (12)/(3)x-(6)/(2)x=18 \\ 4x-3x=18 \\ x=18 \end{gathered}`

Hence, the number is 18.