Problem: With 400 members voting the House of Representatives defeated a bill. A re-vote, with the same members voting, resulted in passage of the bill by twice the margin by which it was originally defeated. The number voting for the bill on the re-vote was 1112​ of the number voting against it originally. How many more members voted for the bill the second time than voted for it the first time?
Answer Choices:
A. 75
B. 60
C. 50
D. 45
E. 20
Solution:
Let y1​,n1​, respectively, represent the numbers voting for, against the bill originally, and let y2​,n2​, respectively, represent the numbers voting for, against the bill on the re-vote.
y1​+n1​∴2(y1​+n1​)∴4n1​∴y2​∴n1​−n2​​=400,y2​+n2​=400,y2​=1112​n1​,y2​−n2​=2(n1​−y1​)=2(y2​+n2​),2(−y1​+n1​)=y2​−n2​=3y2​+n2​=3⋅1112​n1​+n2​∴n1​=811​n2​=1112​⋅811​n2​=23​n2​, so that23​n2​+n2​=400,n2​=160,n1​=220=60,or sincey2​=240andy1​=180,y2​−y1​=60​