VJesus12 wrote: ↑

Thu Sep 16, 2021 11:07 am

Rabia must earn an average (arithmetic mean) score of \(S\) percent to pass her physics course. If her average score on the first \(60\) percent of her assignments was \(S + 10\) percent, and each of her assignments is weighted equally, then what is the maximum percentage below \(S\) that she can earn on her remaining assignments and still pass the course?

A) \(10\%\)
B) \(15\%\)
C) \(20\%\)
D) \(85\%\)
E) \(90\%\)

Answer: B

Source: Princeton Review

We can solve this question using weighted averages:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the average percent score of the remaining 40% of Rabia's assignments
So, for this question, we can write: Average score = (60%)(S + 10) + (40%)(x)
Since we want the total average to be at least S, we can write: S = (60%)(S + 10) + (40%)(x)
Rewrite has: S = (0.6)(S + 10) + (0.4)(x)
Expand to get: S = 0.6S + 6 + 0.4x
Multiply both sides by 10 to get: 10S = 6S + 60 + 4x
Subtract 6S from both sides by 10 to get: 4S = 60 + 4x
Subtract 60 from both sides to get: 4S - 60 = 4x
Divide both sides by 4 to get: S - 15 = x
So, we need an average score of S - 15 on the remaining 40% of the assignments to ensure that Rabia gets a total score of S.

The question asks "What is the maximum percentage below S that she can earn on her remaining assignments and still pass the course?"
Answer: 15 = B


Cheers,
Brent