The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18 . Find the number. -53 35 53 -35

Question

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18 . Find the number.  -53 35 53  -35

Bytelearn · Accepted Answer

Identify Digits: Let's denote the tens digit of the number as x and the units digit as y. The two-digit number can be represented as 10x + y. The number formed by reversing its digits is 10y + x. According to the problem, the sum of the digits is 8, which gives us the equation: x + y = 8Form Equations: The difference between the original number and the reversed number is 18, which gives us the second equation: (10x + y) - (10y + x) = 18 Simplifying this, we get: 9x - 9y = 18 Dividing both sides by 9, we get: x - y = 2Solve System: Now we have a system of two linear equations: 1) x + y = 8 2) x - y = 2 We can solve this system by adding the two equations together to eliminate y. (1) + (2) gives us: x + y + x - y = 8 + 2 2x = 10 Dividing both sides by 2, we get: x = 5Find Tens Digit: Now that we have the value of x, we can substitute it back into one of the original equations to find y. Let's use the first equation: x + y = 8 5 + y = 8 Subtracting 5 from both sides, we get: y = 8 - 5 y = 3Substitute and Calculate: We have found that x (the tens digit) is 5 and y (the units digit) is 3. Therefore, the original two-digit number is: 10x + y = 10*5 + 3 = 50 + 3 = 53

The sum of the digits of a two digit number is $8$ and the difference between the number and that formed by reversing the digits is $18$ . Find the number. $\newline$ $-53$ $\newline$ $35$ $\newline$ $53$ $\newline$ $-35$

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The sum of the digits of a two digit number is 888 and the difference between the number and that formed by reversing the digits is 181818. Find the number.\newline−53-53−53\newline353535\newline535353\newline−35-35−35

The sum of the digits of a two digit number is $8$ and the difference between the number and that formed by reversing the digits is $18$ . Find the number. $\newline$ $-53$ $\newline$ $35$ $\newline$ $53$ $\newline$ $-35$