What method should I use to solve this proportion problem

Here is the problem:

"In an election, 40% of the Democrats and 92.5% of the Republicans voted "yes". Of all the Democrats and Republicans, 68% voted "yes". Find the ratio of Democrats to Republicans."

I came up with 7:8.
I used the substitution method and started with 1:1, 1:2, 2:3, 3:4 etc. until I found something that worked. Is there a method that is more efficient and quick?

Let d be the number of democrats and r be the number of republicans. Then:
0.4d + 0.925r is the total number of yes votes
0.68(d+r) is also the total number of yes votes
so
0.4d + 0.925r = 0.68d + 0.68r
0.28d = 0.245r
d = 0.245/0.28r = 0.875r
d/r = 0.875 = 7/8