SOLUTION: My final test is worth 25 percent of my grade. My homework is worth 15 percent and tests 1-3 are worth 60 percent. If I have a 88 average for my homework and I made a 76 and a 59 o

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Question 884611: My final test is worth 25 percent of my grade. My homework is worth 15 percent and tests 1-3 are worth 60 percent. If I have a 88 average for my homework and I made a 76 and a 59 on two of the tests 1-3 tests what do I need to make on my the 3rd test and on my final to pass?
The lowest passing grade for me to pass would be a 60 out of 100.
A "C" would be at the lowest 70 out of 100.
Show work if willing.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if you look at the following graphs, they will show you what the relationships are that you want to know.
the first graph shows you the scores you need to get a passing grade or above.
the feasible region is the area on the graph bounded by the lines:
y = 100
x = 100
40.2 + .2x + .25y = 60
the value of the x-coordinate is the score you need to attain on the third test.
the value of the y-coordinate is the score you need to attain on the final.
you can pick any coordinate point within the feasible region and you will get an overall grade of 60 or higher in the course.
for example:
you get a 0 on test 3 and an 80 on the final.
your overall grade will be 40.2 + .2*0 + .25 * 80 = 60.2
here's the graph of the feasible region to get at least a 60 overall grade.

here's the graph of the feasible region to get at least a 70 overall grade.

if you want to get an overall grade of at least 70, then the lowest score you can achieve on the third test is 24 and you will also need 100 on the final.
alternatively, the lowest score you can achieve on the final is 39.2 and you will have to get 100 on the third test.
to see how this work, plug the x and y values into the equation expression of 40.2 + .2x + .25y and you will see what the overall score is.
if x = 100 and y = 39.2, the equation becomes 40.2 + .2*100 + .25 * 39.2 = 70.
if x = 24 and y = 100, the equation becomes 40.2 + .2*24 + .25*100 = 70
in order to get a 70 or above, your coordinate point has to be within the feasible region.
the feasible region on this graph is the region bounded by the lines:
x = 100
y = 100
40.2 + .2x + .25y = 70
here's the graph of the feasible region to get at least an 80 overall grade.
same logic applies to the other graphs.
your coordinate point has to be in the feasible region which is the region bounded by the lines:
y = 100
x = 100
40.2 + .2x + .25y = 80
as you will see shortly, the feasible region gets smaller the higher your requirements.

all the graphs are similar except the line of the equation is moved higher if you want to get at least a 70 and higher even still if you want to get a grade of at least 80.
the highest grade you will be able to achieve is if you get 100 on the third test and 100 on the final.
if that happens, your overall grade will be 40.2 + .2*100 + .25*100 = 85.2
it is not possible for you to get better than that.