Illustrate an abstract concept of a vote counting in an election, with three distinct areas. One area, symbolizing the biggest number of votes, comprises 3/7 of the image, painted in bright victorious colours. The second area, symbolizing the runner-up, should occupy 5/8 of the remaining space and is painted with slightly muted colours. The smallest area represents the third candidate and is painted with the least vibrant colours. Furthermore, visually represent the numerical gap of 3021 votes with a separate geometrical shape, connecting the winner's area to the runner-up's. Avoid including any text or numbers.

In an election,there were three candidates 3/7 of the electors voted for the winner.The runner up received 5/8 of the remaining votes.What fractions of the electors voted for the third candidate.If the winner received 3021 votes more than the runner up.How many electors voted.

winner: 3/7, leaving 4/7

runner-up: 5/8 * 4/7 = 5/14
loser: 1 - 3/7 - 5/14 = 3/14
total: 3/7 x = 5/14 x + 3021
...

Let's say that there were x electors in total.

3/7 of them voted for the winner, so that's 3/7x votes.

That leaves 4/7x electors remaining.

The runner-up received 5/8 of the remaining votes, which is (5/8) * (4/7x) = 5/14x votes.

That leaves (4/7x - 5/14x) = 3/14x votes for the third candidate.

We're also told that the winner received 3021 more votes than the runner-up, so:

3/7x = 5/14x + 3021

Multiplying both sides by 14 (the least common multiple of 7 and 2), we get:

6x = 5x + 42,294

Simplifying, we get:

x = 42,294

So there were 42,294 electors in total.

To find out what fraction of the electors voted for the third candidate, we need to divide their votes (3/14x) by the total number of electors (42,294):

(3/14) * (42,294) = 9,078

So 9,078 electors (or 3/14 of the total) voted for the third candidate.

In an election there were three candidates .3/7 of the electors voted for the winner . The runner up received 5/8 of the remaining votes.

A) what fraction of the electors voted for the third cadidate.
B) if the winner recieved 3021 voted than the runner up how many electors voted

I need an answer to this equation

Well, it seems like the electors had quite the circus trying to choose their candidates! Let's juggle some numbers and figure out the answer.

Let's say the total number of electors is represented by the fraction "1" (since we don't know the actual number). According to the given information, 3/7 of the electors voted for the winner.

Now, the remaining votes for the runner-up can be calculated by subtracting the votes of the winner from the total. Since the winner received 3/7 of the votes, the runner-up must have received 1 - 3/7 = 4/7 of the votes.

Next, we're told that the runner-up received 5/8 of the remaining votes. So, if we let "x" represent the number of votes the runner-up received, we can set up an equation: (4/7) * x = 5/8 * (1 - 3/7).

Simplifying that equation, we find: (4/7) * x = 5/8 * (4/7). Don't worry, I won't make you do the math in your head! After some calculations, we find that x = 10/21.

So, the runner-up received 10/21 of the total votes. If the winner received 3021 more votes than the runner-up, we must calculate (3/7 - 10/21) * total votes = 3021.

I don't know about you, but my clown calculator is buzzing with excitement! Solving this equation, we find that the total number of votes is 20580.

Finally, to find the fraction of electors who voted for the third candidate, we need to subtract the votes for the winner and runner-up from the total: 1 - 3/7 - 4/7 = 0/7.

Wait a second... zero over anything is still zero! It seems like none of the electors voted for the third candidate. They must've been too busy juggling other things!

So, in conclusion, the third candidate received zero fraction of the votes. The total number of electors who voted was 20580. I hope that solves the election mystery for you!

To solve this question, we can break it down step-by-step:

Step 1: Find the fraction of electors who voted for the winner
We are given that 3/7 of the electors voted for the winner.

Step 2: Find the fraction of votes received by the runner up
We are also given that the runner up received 5/8 of the remaining votes. This means we need to find the fraction of electors who did not vote for the winner. To do this, we subtract the fraction of votes for the winner from 1 (since all the electors voted), and then multiply by 5/8.

Step 3: Find the fraction of votes received by the third candidate
Since we have already found the fractions of votes received by the winner and the runner up, we can subtract these fractions from 1 to find the fraction of votes received by the third candidate.

Step 4: Calculate the number of votes received by the winner and the runner up
We are given that the winner received 3021 more votes than the runner up. We can use this information with the fractions of votes received by the winner and runner up to set up an equation and solve for the number of votes received by each candidate.

Step 5: Find the total number of electors who voted
We can sum up the votes received by all three candidates to find the total number of electors who voted.

Let's calculate each step:

Step 1:
Fraction of electors who voted for the winner = 3/7

Step 2:
Fraction of votes received by the runner up = (1 - 3/7) * 5/8

Step 3:
Fraction of votes received by the third candidate = 1 - (3/7 + (1 - 3/7) * 5/8)

Step 4:
Let's assume the number of votes received by the runner up is x. Then the number of votes received by the winner would be x + 3021.
Using the fractions from Step 1 and Step 2, we can set up an equation:
(3/7) * E = (1 - 3/7) * 5/8 * E + 3021
Solving this equation will give us the number of votes received by the runner up.

Step 5:
Total number of electors who voted = number of votes received by the winner + number of votes received by the runner up + number of votes received by the third candidate.

Now, let's solve for each step to find the answer.

Good