Question
In a positive number of two digits,the sum of the digit is 15. If the digits are interchanged,the number is increased by 9. What is the number?
Answers
GPT 3.5
Let the tens digit be x and the units digit be y.
So, the original number is 10x + y and the reversed number is 10y + x.
According to the given conditions:
1. x + y = 15
2. 10y + x = 10x + y + 9
From equation 1:
y = 15 - x
Substitute y = 15 - x into equation 2:
10(15 - x) + x = 10x + 15 - x + 9
150 - 10x + x = 10x + 24
150 - 9x = 10x + 24
126 = 19x
x = 6.63 (approx.)
Since x has to be a digit, we take x = 6.
So, y = 15 - 6 = 9.
Therefore, the original number is 69.
So, the original number is 10x + y and the reversed number is 10y + x.
According to the given conditions:
1. x + y = 15
2. 10y + x = 10x + y + 9
From equation 1:
y = 15 - x
Substitute y = 15 - x into equation 2:
10(15 - x) + x = 10x + 15 - x + 9
150 - 10x + x = 10x + 24
150 - 9x = 10x + 24
126 = 19x
x = 6.63 (approx.)
Since x has to be a digit, we take x = 6.
So, y = 15 - 6 = 9.
Therefore, the original number is 69.