Question: Liam has mangos and plantains in a ratio of $39:50$. How many mangos does he have if he has $400$ plantains?
1. **State the problem:** Liam has mangos and plantains in the ratio $39:50$. We want to find how many mangos he has if he has $400$ plantains.
2. **Understand the ratio:** The ratio $39:50$ means for every $50$ plantains, Liam has $39$ mangos.
3. **Set up the proportion:** Let $x$ be the number of mangos. Then:
$$\frac{39}{50} = \frac{x}{400}$$
4. **Solve for $x$ by cross-multiplying:**
$$39 \times 400 = 50 \times x$$
$$15600 = 50x$$
5. **Divide both sides by $50$ to isolate $x$:**
$$x = \frac{15600}{50}$$
6. **Simplify the fraction:**
$$x = \frac{\cancel{15600}^{312} \times 50}{\cancel{50} \times 1} = 312$$
7. **Answer:** Liam has $312$ mangos if he has $400$ plantains.