Question

One eighth of a number is ten less than one third of the number. Find the number.

Answer 1

x/8 - 10 = x/3

bring the values with the variable on one side

x/3 - x/8 = 10

find a common denominator and subtract these fractions

8x/24 - 3x/24 = -10

now subtract fractions

8x - 3x = 5x

5x/24 = -10

multiply both sides by 24

5x = -240

divide both sides by 5

x = -48

the number is -48

Answer 2

`(-5x)/(-5)=(-240)/(-5)`

Explanation:

Let x be our required number.

One-eighth of the number would be
`(1)/(8)x`.

One-third of the number would be
`(1)/(3)x`.

10 less than one-third of the number would be
`(1)/(3)x-10`.

We have been given that one eighth of a number is ten less than one third of the number. We can represent our given information in an equation as:

`(1)/(8)x=(1)/(3)x-10`

`(1)/(8)x-(1)/(3)x=(1)/(3)x-(1)/(3)x-10`

`(x)/(8)-(x)/(3)=-10`

`(3x)/(24)-(8x)/(24)=-10`

`(3x-8x)/(24)=-10`

`(-5x)/(24)=-10`

`(-5x)/(24)*24=-10*24`

`-5x=-240`

`(-5x)/(-5)=(-240)/(-5)`

`x=48`

Therefore, our required number is 48.