Question: User: (80 mg)/(6 mL) = (200 mg)/(x)
1. **State the problem:** We are given the proportion $$\frac{80\text{ mg}}{6\text{ mL}} = \frac{200\text{ mg}}{x}$$ and need to find the value of $x$.
2. **Formula and rule:** To solve for $x$ in a proportion $$\frac{a}{b} = \frac{c}{d}$$, we use cross multiplication: $$a \times d = b \times c$$.
3. **Apply cross multiplication:**
$$80 \times x = 6 \times 200$$
4. **Calculate the right side:**
$$80x = 1200$$
5. **Solve for $x$ by dividing both sides by 80:**
$$x = \frac{1200}{80}$$
6. **Show cancellation:**
$$x = \frac{\cancel{1200}}{\cancel{80}} = 15$$
7. **Final answer:**
$$x = 15\text{ mL}$$
This means that 200 mg corresponds to 15 mL in this proportion.