SOLUTION: Nelson transferred 20 credits with a GPA of 1.5. He has since then earned 25 credits with a GPA of 1.9. What is his overall GPA? How many credits with a 2.5 average would he need t

Algebra ->  Average -> SOLUTION: Nelson transferred 20 credits with a GPA of 1.5. He has since then earned 25 credits with a GPA of 1.9. What is his overall GPA? How many credits with a 2.5 average would he need t      Log On


   



Question 1041634: Nelson transferred 20 credits with a GPA of 1.5. He has since then earned 25 credits with a GPA of 1.9. What is his overall GPA? How many credits with a 2.5 average would he need to raise his GPA to a 2.0?
Please help I am struggling on how to do this

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can imagine the struggle. The sticking point here is
that GPA is being applied to certain restricted grades
( GPA = grades / credits )
--------------------------
Nelson transferred 20 credits with a GPA of 1.5.
+1.5+=+g%5B1%5D+%2F+20+
+g%5B1%5D+=+30+
------------------
Then you are told:
+1.9+=+g%5B2%5D+%2F+25+
+g%5B2%5D+=+47.5+
------------------
Overall GPA = +%28+g%5B1%5D+%2B+g%5B2%5D+%29+%2F+%28+20+%2B+25+%29+
Overall GPA = +%28+30+%2B+47.5+%29+%2F+45+
Overall GPA = +77.5%2F45+
Overall GPA = +1.722+
---------------------------
How many credits with a 2.5 average would he
need to raise his GPA to a 2.0?
Let +n+ = number of credits with 2.5 GPA needed
+2.5+=+g%5B3%5D+%2F+n+
+g%5B3%5D+=+2.5n+
--------------------
New Overall GPA = +%28+g%5B1%5D+%2B+g%5B2%5D+%2B+g%5B3%5D+%29+%2F+%28+20+%2B+25+%2B+n+%29+
+2.0+=+%28+30+%2B+47.5+%2B+2.5n+%29+%2F+%28+45+%2B+n+%29+
+2.0+=+%28+77.5+%2B+2.5n+%29+%2F+%28+45+%2B+n+%29+
+90+%2B+2n+=+77.5+%2B+2.5n+
+.5n+=+12.5+
+n+=+25+
He needs 25 credits with GPA = 2.5 to raise his GPA to 2.0
---------------------------
You could call the GPAs GPA[1], GPA[2], GPA[3] and
the number of credits they apply to n[1], n[2], n[3]
and grades that you get from that
n[1] * GPA[1], n[2]*GPA[2], n[3]*GPA[3]
----------------------------------
Hope I got it and didn't further confuse