1. The problem involves the ratio $5:7$ and some numbers $120$, $4$, and $3$, with variables $x$ and $y$. We need to find the values of $x$ and $y$ that satisfy the given ratio and conditions. 2. The ratio $5:7$ means $\frac{x}{y} = \frac{5}{7}$. 3. From the ratio, we can write $x = \frac{5}{7}y$. 4. If we consider the total parts of the ratio, $5 + 7 = 12$ parts. 5. Given the total quantity related to the ratio is $120$, each part is $\frac{120}{12} = 10$. 6. Therefore, $x = 5 \times 10 = 50$ and $y = 7 \times 10 = 70$. 7. The numbers $4$ and $3$ are not directly related to the ratio problem stated, so we focus on $x$ and $y$. Final answer: $x = 50$, $y = 70$.