Question

Clare asks Andre to play the following number puzzle: Pick a number Add 2 Multiply by 3 Subtract 7 Add your original number Andre’s final result is 27. Which number did he start with?

Answer 1

He started with the number 7.

7+2=9
x3=27
-7=20
+7=27

Answer 2

ANSWER

He started with
$7$


EXPLANATION

Let the number be

$x$



When Andre adds 2, the number becomes,

$x + 2$


When he multiplies by 3, the number becomes,


$3(x + 2)$


When 7 is subtracted, he gets,

$3(x + 2) - 7$


When he adds the original number, he gets,

$3(x + 2) - 7 + x$


We now equate all this to 27,



$3(x + 2) - 7 + x = 27$

We expand brackets to get,

$3x + 6 - 7 + x = 27$

Group like terms,
$3x + x = 27 + 6 - 7$
Simplify,

$4x = 28$

$x = \frac{28}{4}$
$x = 7$


Hence the original number is 7.