The digits of a two-digit number are reversed. When both these two-digit numbers are added, the result is 88, and when subtracted, the result is 54. The original two-digit number contains which of the following digits?
2
3
5
7
Reiny answered this problem earlier today.
http://www.jiskha.com/display.cgi?id=1280241955
To find the original two-digit number, let's assume the tens digit is 'x' and the units digit is 'y'.
According to the given information, the digits of the two-digit number are reversed. So, the reversed number can be represented as 'yx'.
When both the original number and the reversed number are added, the result is 88:
xy + yx = 88
To solve this equation, let's simplify the equation:
xy + yx = 88
10x + y + 10y + x = 88
11x + 11y = 88
x + y = 8
Similarly, when the original number and the reversed number are subtracted, the result is 54:
xy - yx = 54
Simplifying this equation:
xy - yx = 54
10x + y - (10y + x) = 54
9x - 9y = 54
x - y = 6
Now we have a system of two equations:
x + y = 8
x - y = 6
By solving this system of equations, we can find the values of 'x' and 'y'.
Adding these two equations:
(x + y) + (x - y) = 8 + 6
2x = 14
x = 7
Substituting the value of 'x' into one of the equations:
7 - y = 6
y = 7 - 6
y = 1
Therefore, the original two-digit number is 71.
Looking at the answer choices, the original two-digit number contains the digit 1.