1. The problem is to find the value of $x$ in the proportion setup: $$\frac{13}{55} = \frac{100}{x}$$ 2. The formula for solving proportions is to cross multiply: $$a/b = c/d \implies ad = bc$$ 3. Applying cross multiplication here: $$13 \times x = 55 \times 100$$ 4. Simplify the right side: $$13x = 5500$$ 5. To isolate $x$, divide both sides by 13: $$x = \frac{5500}{13}$$ 6. Show the cancellation step: $$x = \frac{\cancel{5500}}{\cancel{13}}$$ (no common factors to cancel, just notation) 7. Calculate the division: $$x \approx 423.08$$ 8. So, the value of $x$ that makes the proportion true is approximately 423.08.