Number of voters (25) Rank First Second Third Fourth5...

In a mayoral election, the number of votes for the incumbent was 25$\%$ more than the number for the opponent. Altogether, the two candidates received 5175 votes. How many votes did the incumbent mayor receive?

If 2/5 of a population voted, that means the rest of um or one minus 2/5 did not vote. That would be 3/5. The population that did not vote and again to change a fraction to a percent simply multiply it by 100%. That will give us 300 over 5% or 60% of the population that did not vote.

And the probability that for the five people on the ballots, they are not arranged enough of you to go old. Okay, so we have went to use the compliment a probability that they're not in alphabetical order. They are in alphabetical order. Is it goes to one minus the probability. God, they are not enough of it. The order, which is off a bit on a compliment. Now, this would be true. One minus. Ah, There's only one way e or fire engine people in alphabetical order. And these five factorial ways off arranging five letters. So this would be wide mine. US one over five. Victoria is under twinned. So one minus under 12. This 119 over 120.

In this problem of water can would for a maximum of three members because Only three members can be elected. So if he votes for just one, so out of five Can we work for 1? That's if he votes for two out of five he has two choices. And If you vote for three so from five yes three choices So have five seats and they don't start choosing and from the five candidates. So this becomes 5 C1 is nothing like five. This is five and your four x 2. I'm actually true is also five and 2. four x 2. This comes as five plus 10 plus 10 which is 25. So the total number of ways in which the person can vote as 20 back not so.

So let's say that we have this voting system where there's a certain amount of points given for each voting place till you vote the place. And this this is such amount points corresponding to that place. For instance, where first was this? 25 points. Now let's say that you earn 51st place those seven second place votes for fourth place votes and 3/10 waste votes, and you want to find the total amount of points you have earned from this voting process. So what we do is we can multiply and the total number of votes by the amount of points. So we have 51st place, which is worth 25 points. Siege then added to seven times the, um about points with second place or 24 plus four times amount of points for fourth place or 22 plus three times amount of points for 10th place. Have a here. We reach a slight problem because we don't know the amount of points for 10th place, so we have to figure out them off points for 10th place, based off the pattern shown. So he always started 25. Then we subtract one sir. Fact one so tracked one. So you always subtracted one. So what we can do is we can write. If fifth place was 21 that's fifth place. What was six place be? What would be 20 and seventh place in 19? Eighth place 18 ninth place 17 and 10th place would be 60. Do you see how that works? Was simply subtract one for each place that we go down. So they are? Yeah. So the amount of points goes down by one for each place that you go down. So we have times 16 over here. Now, we just plugged onto a calculator. So we have 50 times 25 plus seven times 24 because four times 22 plus three times 16 and we end up with 1554. So in this voting process, you earned 1554 points.