Question

Question #1a0d7

Answer 1

`"the number is "36`

Explanation:

If we let the number be represented by n

Change the fractions to eqivalent fractions with a `color(blue)"common denominator"`

`rArr1/3=1/3xx4/4=4/12" and " 1/4=1/4xx3/3=3/12`

`rArr4/12x-3/12x=3larrcolor(red)" difference"`

Since the fractions have a common denominator we can subtract the numerators while leaving the denominator as it is.

`rArr(4x)/12-(3x)/12=x/12`

`rArrx/12=3`

multiply both sides by 12

`cancel(12)^1xxx/cancel(12)^1=12xx3`

`rArrx=36`

`color(blue)"As a check"`

`1/3xx36-1/4xx36=12-9=3to" True"`

`rArr" The number is "36`

Answer 2

36

Explanation:

Let the number be x
One third of the number is `x / 3` and one fourth of the number is `x / 4`. The difference between the two is `x / 3 - x / 4`, which is equal to 3
ie `x / 3 - x / 4 = 3`
The Lowest common Multiple, (LCM) of the denominators namely , is 12
Multiplying through out by 12, we get,

`x / 3 * 12 - x / 4 * 12 = 3 * 12`
or
`4x - 3x = 36`
ie `x = 36`