Question

In the last election, candidate B received twice as many votes as candidate A. Candidate C received 15,000 fewer votes then candidate A. If a total of 109,000 votes were cast, how many votes did candidate B receive?

Answer 1

The votes received by Candidate B is 62000

Solution:

Let "a" be the votes received by candidate A

Let "b" be the votes received by candidate B

Let "c" be the votes received by candidate C

Candidate B received twice as many votes as candidate A

Therefore,

votes received by candidate B = 2(votes received by candidate A)

b = 2a ------- eqn 1

Candidate C received 15,000 fewer votes then candidate A

Therefore,

votes received by candidate C = votes received by candidate A - 15000

c = a - 15000 --------- eqn 2

A total of 109,000 votes were cast.

So we get,

a + b + c = 109000

Substitute eqn 1 and eqn 2 in above equation

a + 2a + a - 15000 = 109000

4a = 109000 + 15000

4a = 124000

a = 31000

Substitute a = 31000 in eqn 1

b = 2a = 2(31000)

b = 62000

Thus votes received by Candidate B is 62000