Give the step-by-step reasoning process and then the final answer. Grady has 20 red numbered cubes and 15 blue numbered cubes. He gives his friend Gage 2/5 of his red numbered cubes and 1/3 of the blue numbered cubes. If Gage had 10 red numbered cubes and 12 blue numbered cubes, find the total number of cubes Gage has?
Grady gave 2 / 5 * 20 cubes = 8 of his red numbered cubes to Gage. If Gage initially had 10 red numbered cubes, his total number of red numbered cubes became 10 cubes + 8 cubes = 18 cubes after Grady gave him 8 more. Grady also gave 1 / 3 * 15 cubes = 5 blue numbered cubes to Gage. This increased Gage's total number of blue numbered cubes to 12 cubes + 5 cubes = 17 cubes. The total number of cubes Gage has is now 17 cubes + 18 cubes = 35 cubes.
The final answer: 35.