### Brain Teasers

# Captain Election

In an election for school captain, 320 votes were cast for five candidates. The winner's margin over the four candidates was 9, 13, 18 and 25. What was the lowest number of votes?

### Answer

52x + (x-9) + (x-13) + (x-18) + (x-25) = 320. Solve this and get x = 77. Therefore the lowest score is 77 - 25 = 52.

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## Comments

Isn't it 52?

I think you're right, Gizzer. You figure it out by calculating the winner's score - call it x. The equation you come up with is: x + (x-9) + (x-13) + (x-1 + (x-25) = 320. Solve this and get x = 77. Therefore the lowest score is 77 - 25 = 52.

Yes 52 and I see what you did wrong glenn!

When you say 51 * 5 + 9 + 13 + 18 + 25 it looks ok at a glance but:

That would give votes of 51 60 64 69 and 76

A difference of 25, 16, 12 and 7 votes.

You took the difference and added it to the lowest vote, but the differences were between the higher vote and the others

When you say 51 * 5 + 9 + 13 + 18 + 25 it looks ok at a glance but:

That would give votes of 51 60 64 69 and 76

A difference of 25, 16, 12 and 7 votes.

You took the difference and added it to the lowest vote, but the differences were between the higher vote and the others

Yep, you are all right, sorry!

Going by the comments it has obviously been edited.

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