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?

Question

2
3
5
7

Explain your reasoning.
How did you come to your conclusion?

Answer 1

original number: 10x+y
reversed number: 10y+x

their sum: 11x + 11y = 88
x+y = 8
their difference: 9x-9y=54
x-y=6

add these two:
2x = 14
x=7
sub back in:
7+y=8
y=1

thus ....

Answer 2

thank you, Mr. Reiny.