Question

How can the number 39 be divided into two parts in order that the sum of `2/3` of one part and `3/4` of the other part is 28?

Answer 1

First part is `15` and other part is `24`

Explanation:

Let the first part be `x`. As sum of two parts is `39`, the other part is `39-x`.

Now `2/3` of first part is `2/3xx x=(2x)/3`

and `3/4` part of other is `3/4xx(39-x)=3/4xx39-3/4xx x=117/4-(3x)/4`

As their sum is `28`, we have

`28=(2x)/3+117/4-(3x)/4`

or `(3x)/4-(2x)/3=117/4-28=117/4-(28xx4)/4`

or `(3x xx3)/(4xx3)-(2x xx4)/(3xx4)=117/4-112/4=5/4`

or `(9x)/12-(8x)/12=5/4`

or `x/12=5/4`

or `x=5/4 xx12=15`

Hence, first part is `15` and other part is `39-15=24`