Question

1/8 of a number is 10 less than 1/3 of the number find the number

Answer 1

Hi there!

Let's first assign a variable to the number. Let's say the number is n. Now, we can write out an equation for this:

We know 1/8 of the number is 10 less than 1/3 of the number. 1/8 of the number is just written as 1/8n. Then, it being 10 less than something means that adding 10 to the expression will make it equal to 1/3 of the number, giving us 1/8n + 10. Now, for 1/3 of the number, that's just written as 1/3n. This all gives us 1/8n + 10 = 1/3n.

Solving:

$\frac{1}{8}n+10=\frac{1}{3}n$

$\frac{3}{24}n+10=\frac{8}{24}n$

$\frac{5}{24}n=10$

$n=10\cdot\frac{24}{5}$

$n=2\cdot24$

$n=48$

Checking this, 1/8 of 48 is 6, and 1/3 of 48 is 16. 6 is to less than 16, meaning we got the answer right, that the number is 16.

Hope this helps!