A number consist of two digits whose sum is 8. if 18 is added to the number its digits are reversed. find the number.
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35
To solve this problem, let's first simplify the given information:
1. The number consists of two digits.
2. The sum of the digits is 8.
3. When 18 is added to the number, its digits are reversed.
Let's break it down step by step:
Step 1: Express the number using variables
Let's assume the tens digit is represented by 'x', and the ones digit is represented by 'y'. Therefore, the number can be expressed as 10x + y.
Step 2: Express the sum of the digits
We are told that the sum of the digits is 8. So, we can write the equation x + y = 8.
Step 3: Express the reversed number
When 18 is added to the original number, the digits are reversed. This means the new number can be expressed as (10y + x) + 18.
Step 4: Set up an equation
Since the number and its reversed form are equal, we can set up the equation 10x + y + 18 = 10y + x.
Step 5: Solve the equations simultaneously
We have two equations:
x + y = 8
10x + y + 18 = 10y + x
We can solve these equations using substitution or elimination method.
Using substitution method:
From the first equation, we have x = 8 - y.
Substituting this value of x into the second equation, we get:
10(8 - y) + y + 18 = 10y + (8 - y)
Simplifying further, we get:
80 - 10y + y + 18 = 10y + 8 - y
Simplifying,
80 + 18 = 20y + 8
98 = 20y
y = 4.9
Since y represents the digit and it must be a whole number, we can assume that y = 4.
Using this value, we can substitute it into the first equation:
x = 8 - y
x = 8 - 4
x = 4
Therefore, the tens digit of the number is 4 and the ones digit is 4.
So, the number is 44.
To check the answer:
If we add 18 to 44, we get 62, which is the reverse of the number 44. Hence, our answer is correct.
a+b = 8
10a+b + 18 = 10b+a
Now just solve for a and b, the two digits.