For mid term grade to be minimum, her final grade should be maximum, as her semester grades are fixed. So, max value value of her final grade will be 100

Now, let her mid term grade be x

0.75*100 + 0.25* x= 88
On solving, x= 52%

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Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee

Hello Vjesus12.

Let's take a look at your question.

Let's call:

m - the grade obtained in the midterm exam
f - the grade obtained in the final exam

m gives 25% of the semester grade and f gives 75%.

We know that Lindsey's semester grade was 88%.

So, we have that $$m\cdot25\%+f\cdot75\%=88\%$$ $$m\cdot0.25+f\cdot0.75=0.88$$ Since we want to know what is the lowest possible score that Lindsey could have received on her midterm exam, then we have to maximize the grade obtained in the final exam.

So, let's suppose that she got 1 in the final exam, hence $$m\cdot0.25+1\cdot0.75=0.88$$ $$m\cdot0.25=0.88-0.75$$ $$m\cdot0.25=0.13$$ $$m=\frac{0.13}{0.25}$$ $$m=0.52.$$ That is to say, the lowest possible score that Lindsey could have in the midterm exam is 52%.

This implies that the correct answer is the option A.

I hope it helps you. <i class="em em-smiley"></i>