1968 AMC 12 Problem 34

Question

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

\dfrac{12}{11}

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?

75

60

50

45

20

Answer: B

Concepts:system of equations ratio and proportion

Difficulty rating: 1900

Small hint:

Let the original and second numbers voting for be

F

and

G

Big hint:

Use

G=\frac{12}{11}(400-F)

and

2G-400=2(400-2F)

Solution:

Let

F,

G

be the original and second numbers voting for the bill. The ratio condition gives

G=\frac{12}{11}(400-F).

The passage margin is twice the original defeat margin, so

2G-400=2(400-2F),

or

G+2F=600.

Solving gives

F=180,

G=240,

so

60

more members voted for it.

Therefore, the correct answer is B.