You need a 35% alcohol solution.

Question

On hand, you have a 300 mL of a 5% alcohol mixture. You also have 60% alcohol mixture. How much of the 60% mixture will you need to add to obtain the desired solution?

Answer 1

V = volume of 60% alcohol mixture

(300 mL * 0.05) + (V * 0.6) = (300 + V) * 0.35

15 + 0.6V = 105 + 0.35V

0.25V = 90

V = 360 mL

Answer 2

Kyle did this the right way (I upvoted him). I'll show you a fun alternative.

35% is 6/11 of the way from 5% to 60%, or it splits the segment from 5% to 60% in the ratio 6:5. Thus, the solution at 60% must be 6/5 the solution at 5% (think balancing see-saws) = 6/5 * 300 = 360.