A number of two digits is increased by 9. when the digits are reversed,the sum of the digit is 5. find the number. help pls
23
Audu Ibrahim
To solve this problem, let's consider a number with two digits:
Let's assume the number is represented as AB, where A is the tens digit and B is the units digit.
According to the problem, when we increase the number by 9, it becomes BA.
To solve the problem, we need to find values for A and B that satisfy the given conditions:
1. When the number AB is increased by 9, it becomes BA.
2. The sum of the digits, A and B, equals 5.
Let's start by examining the first condition: Increasing the number AB by 9 gives BA.
To understand this, let's write the numbers in terms of their place values:
AB = 10A + B
BA = 10B + A
According to the problem, when we increase AB by 9, it becomes BA:
AB + 9 = BA
Substituting the values:
10A + B + 9 = 10B + A
Now let's simplify the equation to isolate A in terms of B:
10A - A = 10B - B - 9
9A = 9B - 9
A = (9B - 9) / 9
A = B - 1
Now that we have an expression for A in terms of B, let's move on to the second condition: The sum of the digits A and B is 5.
A + B = 5
Substituting the value of A from the previous equation:
(B - 1) + B = 5
2B - 1 = 5
2B = 6
B = 3
Now that we have found the value of B, we can substitute it back into the equation to find A:
A = B - 1 = 3 - 1 = 2
So, the number AB is 23.