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:

#10a+b#

Add the digits, gets 12:

1)#a+b=12#

Subtracts the digits, gets 2

2)#a-b=2#

or

3)#b-a=2#

Let's consider equations 1 and 2:

If you add them, you obtain:

#2a=14 => a=7# and #b# must be 5

So the number is 75.

Let's consider equations 1 and 3:

If you add them you obtain:

#2b=14 => b=7# and #a# must be 5,

So the number is 57.