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Find a 3 digit postive interger,the sum of the digits is 14, the tens digit is two more than the ones digit, and if the digits are reversed, the number is unchanged

User AwesomeGuy
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1 Answer

6 votes

Three digit number:
ABC

"if the digits are reversed, the number is unchanged":

A=C, so our number is ABA

"the sum of the digits is 14":

A + B + A = 14 or 2A + B = 14

"the tens digit is two more than the ones digit":

B = A + 2

We have two equations:

2A + B = 14

B = A + 2

Using substitution, we have:

2A + A+2 = 14

3A + 2 = 14

3A = 12

A = 4

Going back to B = A + 2:

B = 4 + 2

B = 6

The number, ABA is 464.

User Ilo
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