Question

Chandrasekhar Subramaayan is taking a course in Astrophysics at the University of Madras. Tomorrow, he will be taking the Final Exam. The Final Exam makes up 65% of the overall average. Chandrasekhar Subramanyan's current average is 74%. What is the lowest score that he can get on the Final Exam that would increase his overall average to a “B”? Show your work.

Answer 1

Final Exam accounts for 65% of total.

The rest is 100 - 65 = 35%

On the 35%, he has 74% or 74 out of 100.

Let's say the final exam is out of 100 and we want to find how much he can afford to get to take him to "B".

Let's say his score needs to be "x" in order to get B.

The overall weighted average of the course would be counted as:

`35\%of74\%+65\%of(x)/(100)=83\%oftotal`

Breaking it down:

74 out of 100 means WHAT out of 35? (let's call the unknown "y")

`(74)/(100)=(y)/(35)`

y would be:

`\begin{gathered} (74)/(100)=(x)/(35) \\ 100x=74\cdot35 \\ x=25.9 \end{gathered}`

So, he currently has 25.9 out of 35.

He would need 83 to get overall average to 83%.

He would need:

83 - 25.9 = 57.1 out of 65

That is:

`(57.1)/(65)\cdot100=87.85\%`

Basically he would need a percentage of 87.85% (MINIMUM) on the final exam to make his overall average to 83% (which is the bare minimum for a B grade).