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4. The sum of the digits of a 2-digit number is 10. If 36 is subtracted from the number, the result is a number whose digits are**
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Question

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## Answers ( )

Answer:73

Step-by-step explanation:Well, let the tens place and ones place digits in the number be respectively and , which are each between 0 and 9 inclusive. Then the number itself is equal to 10+ . Now add 36 to the number, and we have 10++36=10+ , where the last part of the equality follows from the reversal of the digits.

The above equation simplifies to 9+36=9 .

This simplifies to 9(+4)=9 , or +4= .

We need a second equation in order to get a unique solution. The original question says that “the sum of the two-digit number is 10.” This is poorly-worded, but I think what it means is that the sum of the digits in the two-digit number is 10. If that’s true, then +=10 . Since +4=, this becomes 2+4=10 . I.e. 2=6 , or =3 . Thus =+4=7.

The number is 37. Check this answer:

37+36=73

which is indeed a reversal of the digits.