Question

Alice thinks of a number subtracted it from 11 and the multiplies her answer by 5 to get 45. What was the number that Alice started with

Answer 1

`\Huge \boxed{\boxed{x = 2}}`

Explanation:

Let
`x` be the number that Alice started with. We can set up the following equation to represent the situation:

`5(11 - x) = 45`

To solve for
`x`, first divide both sides of the equation by 5:

• 
  `(5(11 - x))/(5) = (45)/(5)`
• 
  `11 - x = 9`

Now, add
`x` to both sides of the equation:

• 
  `11 - x + x = 9 + x`
• 
  `11 = 9 - x`

Subtract 9 from both sides:

• 
  `11 - 9 = 9 + x - 9`
• 
  `2 = x`

So, the number that Alice started with was 2.

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Answer 2

Alice started with the number 2.

Explanation:

Let's call the number that Alice started with
`x`.

According to the problem, Alice first subtracts
`x` from
`11`:

`\large\qquad\qquad\qquad{11 - x}`

She then multiplies this result by 5 to get 45:

`\large\qquad\quad{5(11 - x) = 45}`

Simplifying the equation, we have:

`\large\qquad\quad{55 - 5x = 45}`

Subtracting 55 from both sides, we get:

`\large\qquad\qquad{-5x = -10}`

Dividing both sides by -5, we get:

`\large\qquad\qquad\boxed{\boxed{\bold{\:\:x = 2\:\:}}}`

`\therefore` Alice started with the number 2.