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

`(4)/(x)`

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

`(3)/(x-2)`

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

`(4)/(x)=(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

`(4)/(8)=(1)/(2)`

and that

`(3)/(8-2)=(3)/(6)=(1)/(2)`

so our answer is correct