BTGModeratorVI wrote: ↑Sun Mar 15, 2020 12:43 pm
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
