1. The problem involves comparing two ratios: $7:5:6$ and $4:3:5$, and a number $12$ is given, likely to be used in relation to these ratios. 2. To understand the relationship, we first find the sum of each ratio's parts. - Sum of first ratio parts: $7 + 5 + 6 = 18$ - Sum of second ratio parts: $4 + 3 + 5 = 12$ 3. The number $12$ matches the sum of the second ratio parts, suggesting it represents the total quantity for the second ratio. 4. To find the equivalent total for the first ratio, we set up a proportion based on the sums: $$\frac{18}{x} = \frac{12}{12}$$ Solving for $x$ gives: $$x = \frac{18 \times 12}{12} = 18$$ 5. This means if the second ratio sums to $12$, the first ratio sums to $18$. 6. To find the corresponding parts for the first ratio when the total is $12$, we scale down each part by the factor $\frac{12}{18} = \frac{2}{3}$: - $7 \times \frac{2}{3} = \frac{14}{3} \approx 4.67$ - $5 \times \frac{2}{3} = \frac{10}{3} \approx 3.33$ - $6 \times \frac{2}{3} = 4$ 7. Therefore, the scaled first ratio parts corresponding to a total of $12$ are approximately $4.67 : 3.33 : 4$. Final answer: The first ratio $7:5:6$ scaled to a total of $12$ is approximately $4.67 : 3.33 : 4$.