Yasmin is thinking of a two-digit number. She adds the two digits and gets 12. She subtracts the two digits and gets 2. What was the two-digit number Yasmin was thinking of?

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Answer 1 · 2016-03-08T16:32:05

57 or 75

Two digit number:

$10 a + b$ $10a+b$

Add the digits, gets 12:

1) $a + b = 12$ $a+b=12$

Subtracts the digits, gets 2

2) $a - b = 2$ $a-b=2$

or

3) $b - a = 2$ $b-a=2$

Let's consider equations 1 and 2:

If you add them, you obtain:

$2 a = 14 \Rightarrow a = 7$ $2a=14 => a=7$ and $b$ $b$ must be 5

So the number is 75.

Let's consider equations 1 and 3:

If you add them you obtain:

$2 b = 14 \Rightarrow b = 7$ $2b=14 => b=7$ and $a$ $a$ must be 5,

So the number is 57.