The U. S. senate is composed of 2 senators from each of the 50 states. In order for a treaty to be ratified, at least two thirds of the senators present must approve the treaty. Suppose all senators are present and 48 of them have voted in favor of a treaty. What are the possible numbers of additional senators who must vote in favor of the treaty in order to radify it?

Question

Hugo Reese

Mathematics

10 February, 22:49

The U. S. senate is composed of 2 senators from each of the 50 states. In order for a treaty to be ratified, at least two thirds of the senators present must approve the treaty. Suppose all senators are present and 48 of them have voted in favor of a treaty. What are the possible numbers of additional senators who must vote in favor of the treaty in order to radify it?

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Amber Nolan · Answer 1

So there are 100 senators.

All are present.

You need at least 2/3 of the senators present.

So you need at least 66.66667

66 is not at least 66.66667, 67 is at least 66.66667.

So you need 67 total votes.

You already have 48.

Thus you need an additional 19.

I can't find any trick which would make the number 18.

The question asks for possible numbers which would ratify the treaty

so the answer should be 19, 20, 21, 22 and 52