hey_thr67 wrote: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: 1,000
E: 2,500
Solution:
Since 3/5 means 3 : 5, we first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:
Republicans : Democrats = 3x : 5x
We are given that 600 additional Republicans and 500 additional Democrats registered, and that the new ratio of Republicans to Democrats becomes 4 to 5. It follows that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this information into an equation:
R/D --> (3x + 600)/(5x + 500) = 4/5
After cross multiplying we have:
5(3x + 600) = 4(5x + 500)
15x + 3,000 = 20x + 2,000
1,000 = 5x
x = 200
Thus, after the registration we have the following:
Democrats = (5 × 200) + 500 = 1,500
Republicans = (3 × 200) + 600 = 1,200
There are 1,500 - 1,200 = 300 more Democrats than Republicans.
Answer:
B
