In calvin’s chemistry class, her final grade

As we read the question statement, we instantly realise that this problem is one on finding the weighted average of the lab work and the final exam. One of the fastest approach in solving a weighted average question is to use the alligation diagram.

There are two components which contribute to the final grade – lab work and the final exam. The question says that lab work contributes 2/3rd of the final grade. This means that the final exam contributes 1/3rd of the final grade. The ratio of these two components is 2:1.

Since she wants to earn a final grade of 75% (which represents the average of the final mixture) and she scores 80% in the lab work, we can conclude that she must have scored less than 75% in the final exam.

This is because the Average of any set of quantities will always lie in between the lowest and the highest values.

Since 75% is the average of the final mixture and 80% is the average obtained in lab work, it’s not hard to infer that the average in the final exam should be lower than the average (if she scored higher than 75% in the final exam also, it will violate the rule of averages)

We can plug in all these values into the alligation diagram which will then look like this:



From the alligation diagram,\( \frac{80 – 75 }{ 75 – x} \)= ½ . On simplifying, we get x = 65.

The correct answer option is A.

Hope that helps!

80+80+X= (75*3)
X=65

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In calvin’s chemistry class, her final grade consists of lab work and the final exam. If lab work is 2/3 of the final grade, and she scores 80%, what must she score on the final exam to earn a final grade of 75%?

A)65%

B)68%

C)70%

D)73%

E)75%

weights mentioned if lab work = \(2/3 \)it implies final exam weight = 1 -\(2/3\) = \(1/3\)
lab work/final exam = 2/1
a1 = 80 (lab work %)
a2 = ?
aavg = 75 ( final grade)
\(2/1\) = \(a2-75/75-80\)
\(a2-75/-5\) =\(2/1\)
a2=65
A