What number am I thinking?
Algebra
Level
2
The tens digit of a two-digit number exceeds its units digit by 4. The number exceeds twice the number obtained by reversing the digits of the original number by 10. What is the original number?
The answer is 62.
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1 solution
The two-digit number can be expressed as so:
10(x+4) + x
If the digits were reversed, the new number could be expressed as
10x + (x+4)
We know from the question that the original number is 10 greater than 2 times the original number. As such, we can equate the two.
10(x+4) + x = 2[10x + (x+4)] + 10
Solving for x, we get
11x + 40 = 22x + 18
11x = 22
x = 2
From there, we can substitute x = 2 into the original equation for the number:
10(x+4) + x
=10(2+4) + 2
=62
Therefore, the original number must be 62.