5/8 of votes were blue, 5/9 of remaining were for green and the remaining 48 votes were for red

To answer this you would need to first find out what 3/8 of the 5/9 would be. 3/8 would be the amount that remains after five eights were accounted for. The question says it is 5/9 of the remaining, and 3/8 of the total would be what remains. Multiply 3/8 by 5/9 to get 5/24. This represents the part that would be green. Then I added the original 5/8 for blueand 5/24 for green. The amount is 20/24, or 5/6. This represents the part that is green or blue. 1/6 would be the other color which is red. To find the total, you would solve 1/6x = 48. To solve this divide 48 by 1/6. Keep change and invert your division problem. It would be 48*6. The answer is 288 total votes. You said check your work by multiplying 5/8 by 288. You get 180. 288-180=108. Multiply 5/9 by 108 to get 60. 108-60 is 48!