Hi guys! I'm having trouble answering the following "problem solving" question in my Geometry book?

n = number of votes cast

The candidate received more than 0.94n, but less than 1.00n

This means there must be at least 1 integer > 0.94n and < n

Since n is an integer, then so is n−1.

So n−1 must be > 0.94n and n−1 is obviously < n

n − 1 > 0.94

n − 0.94 n > 1

0.06n > 1

n > 1/0.06

n > 16.667

So the smallest integer > 16.667 is 17

Let n be the number of votes cast, and let r be the number reaped by the candidate in question. Both numbers must be non-negative integers.

94% < r/n < 100%

94 < 100r/n < 100

47/50 < r/n < 1

r/n < 1

r < n

Since r and n are both integers, the maximum of r is n - 1.

47/50 < r/n

(47/50)n < r

(47/50)n < r ≤ n - 1

(47/50)n < n - 1

47n < 50n - 50

50 < 3n

n > 50/3, and n is an integer

n ≥ 17

Let n = 17, r = 16.

r/n = (16/17) ≈ 94.1%

94% < r/n < 100%

The fewest possible number of votes cast is n = 17.

Asked and answered elsewhere. See the source link.

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The president didn't get all the votes (100%), so failed by at least one vote. Then 1 vote is 6% or less of the total number of votes, hence the total number is more than 1/0.06, or 16 2/3. The least integer number more than 16 2/3 is 17.

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It's all about reasoning with numbers. First of all, you need to understand the question. It can help if you just pick some number of votes (say 253, for example) and see what the conditions of the problem mean. In that case, it would mean the president got between 238 and 252 votes, failing to get as many as 15 votes. Clearly, there could have been a smaller number of votes in the election.

Try a smaller number for total votes. After you do this a few times, you should be able to examine the steps you are using and figure out how to figure the smallest possible number.

Let n be the number of students in the school.

Multiply n by 0.94 and round up to the next integer.

The result is the least number of votes cast for the candidate.

For example, if there are 100 students in the school,

0.94×100 = 94

Round up to 95.

The candidate received at least 95 votes and at most 99 votes.

hi! could I have some details of the question and I will try to help you.

I'm an A-level maths student (18yrs old)

More information please.

Edit: For the winner to have received more than 94% but less than 100% of the vote, the one person who voted against them must have a vote worth less than 6% of the total.

1/16 = 0.0625 = 6.25%

1/17 = 0.0588 = 5.88%

So, that's your answer, 17.