Question 623533: please help me figure out this percentage:
there are 4 exams worth 15% each.
and a final exam worth 25 %
here are the scores of the 4 exams: 77.5 %, 80 %, 94%, and 80 %, what must i get on the final exam to achieve atleast an 80% final grade
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4 exams at 15% each equates to 60%
final exam at 25% plus 60% equates to 85%
you only have 85% of your grades covered.
there's 15% missing.
to determine your final grade, you need to include that additional 15%.
it's probably class participation.
make an assumption about what that grade will be and you can then solve your problem easily.
assume your class participation grade is 80%.
then you have 5 grade worth 15% each plus one grade worth 25% (your final exam).
assuming that, your figures come out as follows:
.15 * (sum of all your 5 test grades plus 80% for class participation) is equal to:
.15 * (334.5 + 80) which is equal to:
.15 * 414.5 which is equal to:
62.175
you want a final grade of 80.
62.175 + .25*x = 80
subtract 62.175 from both sides of this equation to get:
.25*x = 80 - 62.175
simplify to get:
.25*x = 17.825
divide both sides of this equation by .25 to get:
x = 17.825 / .25 = 71.3
you need 71.3% on the final exam to get an overall grade of 80 assuming your grade for class participation is equal to 80%.
put this all together, you get:
.15 * (414.5) + .25 * 71.3 = 80
note that .15 * (414.5) is equivalent to:
.15 * (77.5 + 80 + 94 + 80 + 80) which is equivalent to:
.15 * 77.5 + .15 * 80 + .15 * 94 + .15 * 80 + .15 * 80
if you get better than an 80 in class participation, then the grade you need on the final exam is lower.
if you get less than an 80 in class participation, then the grade you need on he final exam is higher.
another way of looking at the formula is:
.15 * (331) + .15 * 80 + .25 * x = 80
the 331 is the total mark on the 4 test you already took.
the 80 is the assumed grade for class participation.
this formula as is would get you x = 71.3
assuming a better grade on class participation would get you the following:
.15 * (331.5) + .15 * 90 + .25 * x = 80
this simplifies to:
49.725 + 13.5 + .25 * x = 80 which further simplifies to:
63.225 + .25 * x = 80
subtract 63.225 from both sides of the equation to get:
.25 * x = 80 - 63.225 = 16.775
divide both sides of the equation by .25 to get:
x = 16.775 / .25 = 67.1
similarly a worse grade on class participation would result in something higher than 71.3
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