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?

Question

Full Questions: 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?

Answer 1

The formula for the new average becomes

(20 credits * 1.5 + 25 credits * 1.9)÷(20 + 25) = Overall GPA

 

(30 + 47.5)÷(45) = 1.72222 = Overall GPA

 

How many credits with a 2.5 average would he need to raise his GPA to a 2.0

 

Let X represent the number of credits needed with a GPA of 2.5 to raise the overall GPA from a 1.72222 to a 2.0

The formula for the new average becomes

(45 credits * 1.72222 + X credits * 2.5)÷(45 + X) = 2.0

(45 credits * 1.72222  + X credits * 2.5) = (45 + X) * 2.0

77.5 +2.5 X= 90+ 2.0 X

 

2.5 X- 2.0 X = 90 - 77.5

 

.5X = 12.5

 

X = 25

 

So he needs 25 credits at 2.5 to raise his GPA from a 1.72222 to a 2

 

(45 credits * 1.72222 + 25 credits *2.5)÷(45+ 25) = Overall GPA

(77.5+ 62.5)÷(70) = Overall GPA

(140)÷(70) = 2.0 = Overall GPA