SOLUTION: IN AN ELECTION BETWEEN A AND B 360 PEOPLE VOTED, A WON. NEXT YEAR B INCREASED HIS VOTES BY 37.5% AND WON BY DOUBLE THE MAJORITY OF A. HOW MANY VOTES B GOT IN FIRST ELECTION?

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Question 896445: IN AN ELECTION BETWEEN A AND B 360 PEOPLE VOTED, A WON. NEXT YEAR B INCREASED HIS VOTES BY 37.5% AND WON BY DOUBLE THE MAJORITY OF A. HOW MANY VOTES B GOT IN FIRST ELECTION?
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
IN AN ELECTION BETWEEN A AND B 360 PEOPLE VOTED, A WON. NEXT YEAR B INCREASED HIS VOTES BY 37.5% AND WON BY DOUBLE THE MAJORITY OF A. HOW MANY VOTES B GOT IN FIRST ELECTION?


Let number of votes B received in 1st election, be B

Then A received: 360 - B votes

Number of votes that A won by (1st election): 360 - B – B, or 360 – 2B



In 2nd election, B increased his number of votes by 37.5%, which means B received 1.375B votes,

in the 2nd election

Since B doubled the number of votes that A had won by in the 1st election, then B won by:

2(360 – 2B), or 720 – 4B votes



Number of votes A received in 2nd election, plus amount of votes B received in 2nd election, equals total votes cast

Number of votes A received in 2nd election: 1.375B

Number of votes B received in 2nd election: 1.375B – (720 – 4B), or 1.375B – 720 + 4B, or 5.375B – 720

Number of votes cast in 2nd election: 360 (same as 1st)

Thus, we get: 1.375B + (5.375B – 720) = 360

1.375B + 5.375B – 720 = 360

1.375B + 5.375B = 360 + 720

6.75B = 1,080

B, or number of votes B received in 1st election = , or  

You can do the check!! 



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