Question

Amrita thinks of a number, she doubles it, adds 9, divides by three and then subtracts one.

She ends up with the same number she had originally, what was her number?
1, 2, 3, 4, or 6?​

Answer 1

I believe your answer would be 6.

Explanation:

I have set up an equation that represents the situation.

Letting the unknown number being 'n':

`(2n+9)/(3) -1=n`

`(2n+9)/(3) -1=n\\\\(2n+9)/(3)-1+1=n+1\\\\(2n+9)/(3)=n+1\\\\(2n+9)/(3)*3=3(n+1)\\\\2n+9=3n+3\\\\2n+9-9=3n+3-9\\\\2n=3n-6\\\\2n-3n=3n-3n-6\\\\-n=-6\\\\(-n)/(-1)=(-6)/(-1)\\\\ \boxed{n=6}`

Answer 2

x = 6

Explanation:

Let the number be x

Now let's make an equation for it:

=>
`(2x+9)/(3) -1 = x`

=>
`(2x+9)/(3) = x+1`

Multiplying both sides by 3

=> 2x+9 = 3(x+1)

=> 2x+9 = 3x+3

=> 3x-2x = 9-3

=> x = 6