Welcome to an example on a Weighted Percentage.
A friend has an 84% average before
the final exam for a course.
That score includes everything but the final,
which counts for 25% of the course grade.
What is the best course grade your friend can earn?
Well the best course grade would be earned
if your friend receives 100% on the final exam
that counts for 25% of the course grade.
Which means the 84% average would be weighted 75%
of the course grade.
And that's because 75% plus 25%
is equal to 100% of the course grade.
In general, to find out weighted percent,
we find the sum of the products of the percent earned
in a particular category times the weight
of that particular category.
Though these percentages do need
to be expressed as decimals.
So, going back to our question,
your friend's grade is going to be equal to
the current average of 84% as a decimal, 0.84
times the weight of 75% as a decimal, that'd be 0.75
plus the best score on the final,
which would be 100% as a decimal,
that would be one or 1.00, if that's helpful.
Times the weight of 25% as a decimal, 0.25.
The sum of this product would be
the best possible course grade.
So we have .84 times .75
plus one times .25, which is .25,
so this gives us 0.88.
As a percentage this should be 88%.
We multiply by 100 and add the percent sign.
So the best possible course grade
for your friend would be 88%.
Next, what is the minimum score your friend would need
on the final to earn a 75% for the course?
Notice here the 75% would be the overall grade or G.
So we'll set this up as an equation.
We'll have 0.75 must equal,
again the current average times 75%, or 0.84
times 0.75
plus now we have an unknown final exam score,
which we'll call X
times 0.25, the weight of the final.
If we solve this equation for X,
we can determine the minimum score needed
to earn 75% for the course.
So we have 0.75 equals
0.84 times
0.75
which gives us 0.63
plus X times 0.25
is 0.25X.
To solve this for X,
we'll first subtract 0.63 from both sides.
So this would give us 0.12
equals 0.25X.
And now we'll divide both sides by 0.25.
So again we have .12 divided by .25,
which gives us 0.48.
Converting back to a percentage this would be 48%.
So if your friend earns 48% on the final,
your friend would receive a grade of 75% for the course.
I hope you found this helpful.