Jenny must sit four papers for an exam. The mean of the first three papers Jenny has sat is 72%.
(a)If she wants to get an overall mean of at least 75%,what is the lowest mark she can get in her fourth paper?
(b) What is the highest possible mean she can get over all four papers?
p1 = paper 1
p2 = paper 2
p3 = paper 3
p4 = paper 4
( a )
The mean of the first three papers Jenny has sat is 72%.
( p1 + p2 + p3 ) / 3 = 72 % Multiply both sides by 3
p1 + p2 + p3 = 72 % * 3 =
p1 + p2 + p3 = 216 %
After 4 papres mean is :
( p1 + p2 + p3 + p4 ) / 4
If she wants to get an overall mean 75% then :
( p1 + p2 + p3 + p4 ) / 4 = 75 % Multiply both sides by 4
( p1 + p2 + p3 ) + p4 = 75 % * 4
216 % + p4 = 300 % Subtract 216 % to both sides
216 % + p4 - 216 % = 300 % - 216 %
p4 = 84 %
( b )
Maximum marks in fourth paper is 100 %.
If p4 = 100 % then :
( p1 + p2 + p3 + p4 ) / 4 =
( p1 + p2 + p3 + 100 % ) / 4 =
( 216 % + 100 % ) / 4 =
316 % / 4 = 79 %
thanks mush
(a) To determine the lowest mark Jenny can get in her fourth paper, we can use the formula for calculating the mean:
Mean = (Sum of all marks) / (Total number of papers)
Let's assume the mark she gets in her fourth paper is x. Given that the mean of the first three papers is 72% and she wants an overall mean of at least 75%, we can set up the following equation:
(72 + 72 + 72 + x) / 4 ≥ 75
Simplifying the equation:
216 + x ≥ 300
Subtracting 216 from both sides:
x ≥ 300 - 216
x ≥ 84
Therefore, the lowest mark Jenny can get in her fourth paper to achieve an overall mean of at least 75% is 84%.
(b) To calculate the highest possible mean she can get over all four papers, we need to maximize the marks on the first three papers and minimize the mark on the fourth paper.
Since the mean of the first three papers is given as 72%, to maximize the mean, Jenny needs to score 100% on each of these three papers. Therefore, the sum of the marks on the first three papers is 100 + 100 + 100 = 300.
Now, let's assume the mark she gets in her fourth paper is y. The equation for calculating the mean is:
Mean = (Sum of all marks) / (Total number of papers)
Therefore, the equation becomes:
(300 + y) / 4 = Mean
Given that the mean needs to be maximized, the denominator (total number of papers) needs to be minimized. Therefore, the highest possible mean occurs when there are only 3 papers.
So the highest possible mean she can get over all four papers is:
Mean = (300 + y) / 4 = (300 + y) / 3, where y is the mark on the fourth paper.
tl;dr
(a) The lowest mark Jenny can get in her fourth paper to achieve an overall mean of at least 75% is 84%.
(b) The highest possible mean she can get over all four papers is (300 + y) / 4 = (300 + y) / 3, where y is the mark on the fourth paper.
To solve this problem, we need to understand how the mean of a set of numbers is calculated and use that information to find the answers.
(a) To find the lowest mark Jenny can get in her fourth paper, we need to consider what the mean of the overall four papers should be. The overall mean is the sum of all the scores divided by the total number of papers.
Let's assume the score on Jenny's fourth paper is x (unknown). The mean of the first three papers is given as 72%.
The sum of the first three papers can be calculated as:
72% + 72% + 72% = 3 * 72%
We know that the overall mean should be at least 75%. So, we can set up an equation:
(3 * 72% + x) / 4 >= 75%
Now we can solve this equation to find the lowest mark Jenny can get on her fourth paper:
(3 * 72% + x) / 4 >= 75%
216% + x >= 300%
x >= 300% - 216%
x >= 84%
Therefore, the lowest mark Jenny can get in her fourth paper to achieve an overall mean of at least 75% is 84%.
(b) To find the highest possible mean Jenny can get over all four papers, we can assume that she scores the maximum possible marks on the first three papers. Let's say the maximum score is 100%.
The sum of the first three papers will be:
100% + 100% + 100% = 3 * 100% = 300%
Now we need to find the minimum possible mark on the fourth paper to achieve the highest possible mean. Using the same equation as before:
(300% + x) / 4 = mean
Since we want the highest possible mean, we need to maximize the value of x. Therefore, we should assume she gets the highest mark on the fourth paper.
x = 100%
So, the highest possible mean Jenny can get over all four papers is:
(300% + 100%) / 4 = 400% / 4 = 100%
Therefore, the highest possible mean Jenny can get over all four papers is 100%.