1. **State the problem:** Apples cost $x$ cents each and oranges cost $(x + 2)$ cents each. Dylan spends 323 cents on apples and 323 cents on oranges. The total number of apples and oranges bought is 36. 2. **Define variables:** Let the number of apples be $a$ and the number of oranges be $o$. 3. **Write equations from the problem:** Cost of apples: $a \times x = 323$ Cost of oranges: $o \times (x + 2) = 323$ Total fruits: $a + o = 36$ 4. **Express $a$ and $o$ in terms of $x$:** From apples: $a = \frac{323}{x}$ From oranges: $o = \frac{323}{x + 2}$ 5. **Use total fruits equation:** $$\frac{323}{x} + \frac{323}{x + 2} = 36$$ 6. **Multiply both sides by $x(x+2)$ to clear denominators:** $$323(x + 2) + 323x = 36x(x + 2)$$ 7. **Expand and simplify:** $$323x + 646 + 323x = 36x^2 + 72x$$ $$646x + 646 = 36x^2 + 72x$$ 8. **Bring all terms to one side:** $$36x^2 + 72x - 646x - 646 = 0$$ $$36x^2 - 574x - 646 = 0$$ 9. **Divide entire equation by 2 for simplification:** $$18x^2 - 287x - 323 = 0$$ **Final answer:** The equation in $x$ is $$18x^2 - 287x - 323 = 0$$.