The sum of a two-digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number. URGENT!!!
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Let us assume x and y are the two digits of the two-digit number
Therefore, the two-digit number = 10x + y and reversed number = 10y + x
Given:
10x + y + 10y + x = 132
11x + 11y = 132
x + y = 12 ---------------1
Also given:
10x + y + 12 = 5 (x + y)
10x + y + 12 = 5x + 5y
4y - 5x = 12 ------------2
Multiply equation 1 by 5
5x + 5y = 60 ------------3
Adding equation 2 and equation 3
9y = 72
y = 8
Therefore x = 12 - y = 12 - 8 = 4
The two digit number is = 10x + y = 10 * 4 + 8 = 48
Therefore, the two-digit number = 10x + y and reversed number = 10y + x
Given:
10x + y + 10y + x = 132
11x + 11y = 132
x + y = 12 ---------------1
Also given:
10x + y + 12 = 5 (x + y)
10x + y + 12 = 5x + 5y
4y - 5x = 12 ------------2
Multiply equation 1 by 5
5x + 5y = 60 ------------3
Adding equation 2 and equation 3
9y = 72
y = 8
Therefore x = 12 - y = 12 - 8 = 4
The two digit number is = 10x + y = 10 * 4 + 8 = 48
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