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Figure This!


Complete Solution:

Assume winning means a simple majority or over half of the votes. If it takes at least half voting Yes to pass a motion, the motion did not pass.

There are different ways to solve the problem.

Look at different numbers of boys and girls. Think about each of the following:

  1. A class of 50 boys and 50 girls

  2. A class of 0 boys and 100 girls

  3. A class of 100 boys and 0 girls

In neither of the extreme cases nor in any other case will the motion pass.


Alternate Solution 1:

Think about a line diagram showing the percentages where the numbers of boys and girls are not the same:

Above the line, you see that 100% of the boys are depicted to the left of the bold line [light blue rectangle] with 100% of the girls to the right [pink rectangle]. Below the line are the voting percentages of Yes and No for both boys and girls.

To determine if the Yes vote wins, then the segments representing the Yes votes together have to be over half the length of the entire segment. The segments representing Yes will never add to half of the total length so the motion cannot pass.


Alternate Solution 2:

Think about the percentage who voted No: 78% of the girls voted No; 70% of the boys voted No. There is no way for over half of the total to vote Yes.

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