1. **Problem 4:** Lena is buying a soft toy costing 10 dollars with a 40% sales tax. We want to find equations that can be used to find the total amount paid. 2. The total amount paid is the price plus 40% of the price. The sales tax is 40% of 10 dollars, which is $0.40 \times 10 = 4$ dollars. 3. The total amount paid is $10 + 4 = 14$ dollars. 4. To find the total amount using proportions, we can set up ratios comparing parts to wholes. For example, the ratio of total price to base price is $\frac{14}{10}$. 5. Let's analyze each equation: - A: $\frac{140}{x} = \frac{100}{10}$ simplifies to $\frac{14}{x} = \frac{10}{1}$ after dividing numerator and denominator by 10. This does not match the ratio $\frac{14}{10}$. - B: $\frac{10}{x} = \frac{100}{140}$ simplifies to $\frac{10}{x} = \frac{10}{14}$ after dividing numerator and denominator by 10. Cross-multiplying gives $10 \times 14 = 10 \times x$ or $140 = 10x$, so $x = 14$. This matches the total amount. - C: $\frac{140}{x} = \frac{10}{10}$ simplifies to $\frac{14}{x} = 1$. Cross-multiplying gives $14 = x$, which matches the total amount. - D: $\frac{14}{x} = \frac{100}{10}$ simplifies to $\frac{14}{x} = 10$. Cross-multiplying gives $14 = 10x$, so $x = \frac{14}{10} = 1.4$, which does not match the total amount. 6. Therefore, equations B and C can be used to find the total amount paid. --- **Final answer:** Equations B and C are correct.