Question

The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

Answer 1

The original two-digit number described in the problem is 46.

Step-by-step explanation:

Let the two-digit number be 10x + y (where x is the tens digit and y is the units digit). The number formed by interchanging the digits would be 10y + x. According to the problem, the the sum of these two numbers equals 110. So, 10x + y + 10y + x = 110, which simplifies to 11x + 11y = 110 and x + y = 10. The second condition states if 10 is subtracted from the first number, it equals 4 more than 5 times the sum of the digits, meaning that (10x + y) - 10 = 5(x + y) + 4, which simplifies to 5x - 4 = 0, from which we can determine that x = 4. Substitute x = 4 into x + y = 10, we find that y = 6. So, the original two-digit number is 46.

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