SOLUTION: Four times the ones digit of a positive, two digit integer is 25 greater than the sum of the digits. Reversing the digits increases the number by 63. What is the number?

Question 1153592: Four times the ones digit of a positive, two digit integer is 25 greater than the sum of the digits. Reversing the digits increases the number by 63. What is the number?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
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Four times the ones digit of a positive, two digit integer is 25 greater than the sum of the digits. Reversing the digits increases the number by 63. What is the number?
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u, the ones digit
t, the tens digit
u+10t, the two-digit number

The description:

Simplify.

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-

Finish to solve.

The number is 29.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a quick path to the answer, if a formal algebraic solution is not required.

The difference between a 2-digit number and the 2-digit number with the digits reversed is 9 times the difference of the two digits.

The given number is increased by 63 = 9*7 when the digits are reversed, so the difference between the digits is 7. That means the 2-digit number can be only 18 or 29.

18 doesn't satisfy the condition that the ones digit is 25 more than the sum of the digits; 29 does.

ANSWER: 29

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