Problem

출제율 85\%
십의 자리의 숫자가 일의 자리의 숫자보다 1 만큼 작은 두 자리의 자연수가 있다. 이 자연수는 각 자리의 숫자 의 합의 5 배와 같다고 할 때, 이 자연수를 구하시오.

Answer

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Answer

\(\boxed{45}\) is the two-digit number.

Steps

Step 1 :Let the tens digit be x and the units digit be y. We know that \(x = y - 1\) and the number itself can be represented as \(10x + y\). The sum of the digits is \(x + y\).

Step 2 :We are given that the sum of the digits \((x + y)\) is equal to one-fifth of the number itself \((10x + y)\). So, we can write the equation: \(x + y = \frac{1}{5} (10x + y)\).

Step 3 :Solve the equation to find the values of x and y: \[\begin{cases} x = y - 1 \\ x + y = 2.0x + 0.2y \end{cases}\]

Step 4 :The solutions are \(x = 4\) and \(y = 5\).

Step 5 :\(\boxed{45}\) is the two-digit number.

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