Question

Three candidates were running for president of a student council. Altogether, 1524 students cast a vote in the election. The second place candidate had 140 votes less than the winner, but 395 votes more than the last place candidate. What percentage of all the votes cast were received by the winner? (Round your answer to the nearest percent).

Answer 1

Answer:

48%

Step-by-step explanation:

The total number of votes casted = 1524 votes = 100%

Let a = votes of first place candidate

b = votes of second place candidate

c = votes of third place candidate

The second place candidate had 140 votes less than the winner

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

a + b + c = 1524 votes....... Equation 5

If a = b + 140 and c = b - 395

The number of votes by b(second place candidate ) =

b + 140 + b + b - 395 = 1524 votes

3b = 1524 + 395 - 140

3b = 1779

b = 1779/3

b = 593 votes.

Therefore, the second place candidate had 593 votes.

Now we can calculate how many votes, the other candidates had.

The second place candidate had 140 votes less than the winner

Votes for the winner( first place candidate)

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Since b = 593

a = 593 + 140

a = 733 votes

Votes for the last place candidate

Since, Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

b = 593

c = 593 - 395

c = 198

From the above calculation,

a = votes of first place (winner) candidate = 733

b = votes of second place candidate = 593

c = votes of third(last) place candidate = 198

In the above question, we were asked to calculate the percentage of all the votes cast were received by the winner.

This is calculated as

= Voted received by winner/ Total number of votes casted × 100

= 733/1524 × 100

= 48.09711286%

Approximately to the nearest percent = 48%

Therefore, the percentage of all the votes cast were received by the winner = 48%