Simultaneous Equations!!! Exciting?

Question

in an election for school captain, 320 votes were cast for 5 candidates. the winner's margins over the 4 candidates were 9,13,18 and 25. what was the lowest number of votes recieved by a candidate?

Answer 1

52

52+
59+
64+
68+
77
==320

320 = x + (x-9) + (x-13) + (x-18) + (x-25)
320 = 5x -65
385 = 5x
77 = x

x-25= lowest #
77-25 = 52

Answer 2

The answer will definitely be 51...

Solution:

Let the lowest number of votes be x.

thus,
Candidate A: x (he will be the lowest)
Candidate B: x+9
Candidate C: x+13
Candidate D: x+18
Candidate E: x+25 (he's the highest-winner)

the sum of all votes will be 320... hence..

x + (x+9) + (x+13) + (x+18) + (x+25) = 320
5x + 65 = 320
5x = 320-65
5x = 255
x = 255/5
= 51

The lowest number of votes received by a candidate is 51 votes...

This explanation should be sufficient for you to understand how the answer is being derived...

cheers.. (",)

Answer 3

52 see solution below
---------------------------------
the highest number is N
the lowest number is N-25
next is N-18
next N-13
next N-9
N+N-25+N-18+N-13+N-9=320
5N-25-18-13-9=320
5N=320+65=385
N=385/5=77
loswest number of votes is 52,
the number of votes are:
77, 68, 64, 59, 52
77+68+64+59+52=320

Answer 4

Let
x = votes of winner
Votes of losers
x - 9
x - 13
x - 18
x - 25

x + x - 9 + x - 13 + x - 18 + x - 25 = 320
5x - 65 = 320
x - 13 = 64
x = 77

Lowest
x - 25 = 52

^_^

Answer 5

the lowest number of votes received by a candidate is 52
the candidates receive the following votes in increasing order

52
59
64
68
77

Answer 6

x + (x + 9) + (x + 13) + (x + 18) + (x + 25) = 320
5x + 65 = 320
5x = 255
x = 51

51, 60, 64, 69, 71

ANS : 51 votes

Answer 7

51?