1. **State the problem:** Dylan buys apples costing $x$ cents each and oranges costing $(x+2)$ cents each. He 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:** From the cost of apples: $$a \times x = 323$$ From the cost of oranges: $$o \times (x+2) = 323$$ From the total number of fruits: $$a + o = 36$$ 4. **Express $a$ and $o$ in terms of $x$:** $$a = \frac{323}{x}$$ $$o = \frac{323}{x+2}$$ 5. **Use the total number equation:** $$a + o = 36$$ Substitute $a$ and $o$: $$\frac{323}{x} + \frac{323}{x+2} = 36$$ 6. **Multiply both sides by $x(x+2)$ to clear denominators:** $$323(x+2) + 323x = 36x(x+2)$$ 7. **Expand both sides:** $$323x + 646 + 323x = 36x^2 + 72x$$ 8. **Combine like terms on the left:** $$646x + 646 = 36x^2 + 72x$$ 9. **Bring all terms to one side:** $$0 = 36x^2 + 72x - 646x - 646$$ $$0 = 36x^2 - 574x - 646$$ 10. **Simplify by dividing all terms by 2:** $$0 = 18x^2 - 287x - 323$$ **Final equation:** $$18x^2 - 287x - 323 = 0$$