Question: 12. In a recipe, the ratio of flour to sugar is 4:1. If 16 cups of flour are used, how many cups of sugar are needed?
1. **State the problem:** The ratio of flour to sugar is $4:1$. We have $16$ cups of flour and want to find the amount of sugar needed.
2. **Formula and rule:** If the ratio of flour to sugar is $4:1$, then for every $4$ parts of flour, there is $1$ part of sugar.
3. **Set up the proportion:** $$\frac{\text{flour}}{\text{sugar}} = \frac{4}{1} = \frac{16}{x}$$ where $x$ is the cups of sugar.
4. **Solve for $x$:**
$$4 = \frac{16}{x}$$
Multiply both sides by $x$:
$$4x = 16$$
Divide both sides by $4$:
$$x = \frac{16}{\cancel{4}} = 4$$
5. **Answer:** The amount of sugar needed is $4$ cups.
**Final answer: 4 cups of sugar (Option B).