Translate the following word problems into algebraic systems and solve:

1. The sum of two numbers is 25, and their difference is 7. Find the numbers.
2. Three apples and two oranges cost 55 cents. Two apples and four oranges cost 70 cents. Find the cost of one apple and one orange.
3. If 2 is added to both the numerator and denominator of a fraction, its value becomes \(\frac{2}{3}\). If 3 is subtracted from both, its value becomes \(\frac{1}{2}\). Find the original fraction.