# algebra

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

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1. 53

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2. Sum = 8 = 7+1 = 6+2 = 5+3 = 4+4
Select 5, and 3:
Original #: 53.
Reversed: 35.
Difference = 53-35 = 18.

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posted by Henry
3. Here is how you do this with algebra.
Let x = 10s digit
and y = units digit.
So the number is 10x + y
and you know that if you reverse the number it is 10y + x.
The problem tells you that
10x + y = 10y+x+18 which simplifies to
9x-9y=18
The second equation is x + y = 8. Solve those two equations simultaneously this way.
9x-9y = 18
x+y=8
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Multiply equation 2 by 9 and you have these two equations.
9x - 9y = 18
9x + 9y = 72
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18x = 90
x = 90/18 = 5 which is the 10s digit.

Since x + y = 8, then
5 + y = 8 and y = 8-5=3 which is the units digit so the number is 53

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