Question

the ratio of democrats to republicans in a certain state legislature is 5:7. if the legislature has 156 members, all of whom are either democrats or republicans (but not both), what is the difference between the number of republicans and the number of democrats?

Answer 1

91 Republicans, 65 Democrats

The difference is 26.

Explanation:

Let d be the number of Democrats and r be the number of Republicans. We have

d/r = 5/7, so d = (5/7)r

r + (5/7)r = 156

(12/7)r = 156

r = 91, d = 65, so r - d = 26