Select the correct answerThe sum of two digits of a number is 15. if 9 is added to the number, the digit is reversed. The numbers are?
Question
Select the correct answer
The sum of two digits of a number is 15. If 9 is added to the number, the digit is reversed. The numbers are?
Solution
The problem is asking for a two-digit number where the sum of the digits is 15 and when 9 is added to the number, the digits are reversed.
Let's denote the tens digit as "a" and the units digit as "b".
From the problem, we know that:
- a + b = 15
- 10a + b + 9 = 10b + a
We can simplify the second equation to:
9a - 9b = -9
Divide the entire equation by 9, we get:
a - b = -1
Now we have a system of two equations:
a + b = 15 a - b = -1
Solving this system, we get a = 7 and b = 8.
So, the number is 78.
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