Problem Solving

aditya67 wrote: ↑

Wed Mar 25, 2020 10:24 am

In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?
(a)100
(b)300
(c)400
(d)1000
(e) 2500

We can let 4x and 5x be the new numbers of Repulbican and Democratic voters after the additional voters from both parties, respectively. We can create the equation:

(4x - 600)/(5x - 500) = 3/5

5(4x - 600) = 3(5x - 500)

20x - 3000 = 15x - 1500

5x = 1500

x = 300

Therefore, after the additional voters from both parties, there are 4(300) = 1200 Republicans and 5(300) = 1500 Democrats. We see that the number of Democrats is 300 more than that of Republicans.

Answer: B