For a recent session, there were 9 more Democrats than Republicans in a state senate. This resulted in a ratio of 8 Democrats to 5 Republicans.

Question

For a recent session, there were 9 more Democrats than Republicans in a state senate. This resulted in a ratio of 8 Democrats to 5 Republicans. How many senators were Democrat and how many were Republican?

Answer 1

D = 9 +R

R=D-9

D/R = 8/5 cross multiply

5D = 8R substitute 9+R for D

5D = 5(9+R) = 45 +5R subtract to get

0=3R -45

R = 45/3 = 15 Republicans

D = 24 Democrats. 24/15 = 8(3)/5(3) = 8/5