Question

If 4 is divided by a number is equal to 3 divided by the number decreased by 2,find the number.

Answer 1

let x be our number. So we have the following expression

$\frac{4}{x}$

as "divided by a number". As for "the number decreased by 2" we have x-2. So we also have the expression

$\frac{3}{x-2}$

We are told that this 2 expressions are equal, so we have the equation

$\frac{4}{x}=\frac{3}{x-2}$

which is equivalent to the equation

$4\cdot(x-2)=3\cdot x$

If we distribute on the left side, we get

$4x-8=3x$

Now, we add 8 on both sides, so we get

$4x=3x+8$

Finally, we subtract 3x on both sides

$8=4x-3x=x$

So our number is x=8. We can check that

$\frac{4}{8}=\frac{1}{2}$

and that

$\frac{3}{8-2}=\frac{3}{6}=\frac{1}{2}$

so our answer is correct