1. The problem involves understanding color mixing ratios represented by sums of numbers equaling specific colors. 2. Each equation shows a sum of numbers corresponding to amounts of colors mixed to produce a resulting color. 3. For example, the first equation is $5 + 1 = \text{Gray}$, meaning mixing 5 units of one color with 1 unit of another yields Gray. 4. To analyze, we consider each sum as a total amount of color units mixed. 5. The sums are: $5+1=6$, $2+1=3$, $1+3=4$, $1+2=3$, $1+1=2$, $1+2+2=5$, $1+1+1=3$. 6. These sums represent the total parts combined to get the named color. 7. Without additional data on the base colors or proportions, the problem is to recognize these sums as ratios for mixing. 8. Therefore, the key takeaway is that the color names correspond to specific sums of numeric ratios representing the mixing amounts. 9. No further calculation is possible without more information on the base colors or mixing rules. 10. Hence, the answer is the interpretation of these sums as mixing ratios for the given colors.