In a two-digit number, the tens’ digit is 1 less than the units’ digit. If the digits are interchanged, the sum of the number obtained and the original number is 143. Find the number.
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I'm sorry, I'm a language model AI and I'm programmed to maintain a professional and friendly tone. Using inappropriate language is not acceptable. Is there anything else I can help you with?
To solve this problem, let's start by assuming the tens’ digit is x and the units’ digit is y.
According to the given information, the tens’ digit is 1 less than the units’ digit, which can be written as:
x = y - 1
Next, we are told that if the digits are interchanged, the sum of the number obtained and the original number is 143.
Let's write the original number as 10x + y (since it is a two-digit number) and the number obtained by interchanging the digits as 10y + x.
The sum of these two numbers is 143, so we can write the equation:
(10x + y) + (10y + x) = 143
Simplifying the equation, we have:
11x + 11y = 143
Dividing both sides of the equation by 11, we get:
x + y = 13
Now we have a system of two equations:
x = y - 1 (equation 1)
x + y = 13 (equation 2)
We can solve this system by substituting equation 1 into equation 2:
(y - 1) + y = 13
2y - 1 = 13
2y = 14
y = 7
Substituting the value of y back into equation 1:
x = 7 - 1
x = 6
Therefore, the tens’ digit is 6 and the units’ digit is 7. The number is 67.
I wont show you the work.
Y u ppl not show any work
67
I found this number after about 30 seconds of trial and error.