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A number consist of two digits whose sum is 10. If 54 is added to the number, the order of the digits will be reversed. What is the number?
Let me see.
Let the ones digit of a two-digit number be x and tens digits to be y. Then the sum of the number is x+10y.
Reversing the digits we get y + 10x.
54 + x + 10y = y + 10x
54 + 10y = 10x - x
54 + 10y = 9x
54 = 8x - 10y
Our two systems of equations are
x + y = 10
8x - 10y = 54
Correct system? The answer is 28.
Let me see.
Let the ones digit of a two-digit number be x and tens digits to be y. Then the sum of the number is x+10y.
Reversing the digits we get y + 10x.
54 + x + 10y = y + 10x
54 + 10y = 10x - x
54 + 10y = 9x
54 = 8x - 10y
Our two systems of equations are
x + y = 10
8x - 10y = 54
Correct system? The answer is 28.
