Question: 12mg ______ 102mg
___________ = ______________
5 tabs x
1. **State the problem:** We are given a proportion comparing amounts of medication and number of tabs:
$$\frac{12\text{ mg}}{5\text{ tabs}} = \frac{102\text{ mg}}{x}$$
We need to find the value of $x$, the number of tabs corresponding to $102$ mg.
2. **Formula used:** For proportions, the cross products are equal:
$$a/b = c/d \implies a \times d = b \times c$$
3. **Apply the formula:**
$$12 \times x = 5 \times 102$$
4. **Calculate the right side:**
$$5 \times 102 = 510$$
So,
$$12x = 510$$
5. **Solve for $x$ by dividing both sides by 12:**
$$x = \frac{510}{12}$$
6. **Simplify the fraction:**
$$x = \frac{\cancel{510}}{\cancel{12}} = \frac{85}{2.0} = 42.5$$
7. **Interpretation:**
$x = 42.5$ tabs. Since the number of tabs usually must be whole, this suggests approximately $43$ tabs are needed for $102$ mg.
**Final answer:**
$$x = 42.5\text{ tabs}$$