Say I have five solutions of various concentrations such as the below:

A = 16%
B = 12%
C = 12.5%
D = 17%
E = 5%


Their quantities do not matter, only their concentrations. Say I want to mix them and the final spread between them should follow a ratio of 1:2:1:2:6. Is this enough information given to determine the final % of each solution in the final mixture? If so, how would I calculate the final %s of each solution?

Riista..based on your description, if you know the dilution ratios, then since each solution contains a different solute, each solution is a relative dilutant to the others. For example, the concentration of A after mixing with your ratios will be: $\frac{1\cdot16\%}{1+2+1+2+6=12}$. In general, the final % will be $\frac{ratio \cdot conc.\%}{12}$
What do you mean spread? Is the concentration for each solution representing the percentage of the same thing in each one, so A is $16\%$ something, E is $5\%$ the same thing and you want the final percentage if you mix the ratio you give? If so, you just need a weighted average of the percentages, weighted by the proportion of each solution. It would be $\frac {1 \cdot 16+2\cdot 12 + \dots}{1+2+\dots}\%$ I'll leave the dots to you