At ABB China college of 2017, Shivam, a new candidate has taken 10 courses, earning grades P (worth 4 points each), Q (worth 3 points e

Question

At ABB China college of 2017, Shivam, a new candidate has taken 10 courses, earning grades
P (worth 4 points each), Q (worth 3 points each) and R (worth 2 points each). His grade point
average is 3.2, and if the course in which he get R’s were deleted, his GPA in the remaining
courses would be 3.333. How many P’s, Q’s and R’s did he get?​

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2 months 2021-11-23T06:09:57+00:00 2 Answers 0 views 0

1. Let say P’s  = x

and Q’s  = y

then R’s = 10 -(x + y)

Score = (4x + 3y  + 2(10 – x – y)) / 10  = 3.2

=> 4x + 3y + 20 -2x – 2y = 32

=> 2x + y  = 12

R’s were deleted    ( 3.333  = 10/3)

=> (4x + 3y)/(x + y)  = 10/3

=> 12x + 9y = 10x + 10y

=> 2x = y

2x + y  = 12

=> y + y = 12

=> 2y = 12

=> y =  6

=> x = 3

P’s  =  3

Q’s  = 6

R’s = 10 -(3 + 6) = 1

2. Given : taken 10 courses, earning grades P (worth 4 points each), Q (worth 3 points each) and R (worth 2 points each).

His grade point average is 3.2.

if the course in which he get R’s were deleted, his GPA in the remaining

courses would be 3.333

To Find :  How many P’s, Q’s and R’s did he get?​

Solution:

Let say P’s  = x

and Q’s  = y

then R’s = 10 -(x + y)

Score = (4x + 3y  + 2(10 – x – y)) / 10  = 3.2

=> 4x + 3y + 20 -2x – 2y = 32

=> 2x + y  = 12

R’s were deleted    ( 3.333  = 10/3)

=> (4x + 3y)/(x + y)  = 10/3

=> 12x + 9y = 10x + 10y

=> 2x = y

2x + y  = 12

=> y + y = 12

=> 2y = 12

=> y =  6

=> x = 3

P’s  =  3

Q’s  = 6

R’s = 10 -(3 + 6) = 1