1. **Stating the problem:** We know that 42 meters of fabric cost 1050 euros. We want to find out how many meters of fabric can be bought with 450 euros. 2. **Formula used:** The cost is proportional to the length of fabric. We use the formula for direct proportionality: $$\frac{\text{Cost}_1}{\text{Length}_1} = \frac{\text{Cost}_2}{\text{Length}_2}$$ 3. **Set up the equation:** $$\frac{1050}{42} = \frac{450}{x}$$ where $x$ is the unknown length of fabric for 450 euros. 4. **Solve for $x$:** Multiply both sides by $x$: $$x \cdot \frac{1050}{42} = 450$$ Divide both sides by $\frac{1050}{42}$: $$x = \frac{450}{\frac{1050}{42}}$$ Show the cancellation step: $$x = 450 \cdot \frac{42}{\cancel{1050}} \cdot \frac{\cancel{1050}}{1050} = 450 \cdot \frac{42}{1050}$$ Simplify the fraction $\frac{42}{1050}$: $$\frac{42}{1050} = \frac{42 \div 42}{1050 \div 42} = \frac{1}{25}$$ So, $$x = 450 \times \frac{1}{25} = \frac{450}{25} = 18$$ 5. **Answer:** With 450 euros, you can buy **18 meters** of fabric.