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

Answer:

$\frac{-5x}{-5}=\frac{-240}{-5}$

Step-by-step explanation:

Let x be our required number.

One-eighth of the number would be $\frac{1}{8}x$.

One-third of the number would be $\frac{1}{3}x$.

10 less than one-third of the number would be $\frac{1}{3}x-10$.

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:

$\frac{1}{8}x=\frac{1}{3}x-10$

$\frac{1}{8}x-\frac{1}{3}x=\frac{1}{3}x-\frac{1}{3}x-10$

$\frac{x}{8}-\frac{x}{3}=-10$

$\frac{3x}{24}-\frac{8x}{24}=-10$

$\frac{3x-8x}{24}=-10$

$\frac{-5x}{24}=-10$

$\frac{-5x}{24}*24=-10*24$

$-5x=-240$

$\frac{-5x}{-5}=\frac{-240}{-5}$

$x=48$

Therefore, our required number is 48.