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In a certain history class of 17 juniors and seniors, each j
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19 Jun 2020, 09:53
19 Jun 2020, 09:53
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90% (00:56) correct
9% (01:01) wrong based on 21 sessions
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In a certain history class of 17 juniors and seniors, each junior has written 2 book reports and each senior has written 3 book reports. If the 17 students have written a total of 44 book reports, how many juniors are in the class?
A. 7
B. 8
C. 9
D. 10
E. 11
A. 7
B. 8
C. 9
D. 10
E. 11
Re: In a certain history class of 17 juniors and seniors, each j
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19 Jun 2020, 09:54
19 Jun 2020, 09:54
Expert Reply
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Re: In a certain history class of 17 juniors and seniors, each j
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19 Jun 2020, 10:04
19 Jun 2020, 10:04
1
Carcass wrote:
In a certain history class of 17 juniors and seniors, each junior has written 2 book reports and each senior has written 3 book reports. If the 17 students have written a total of 44 book reports, how many juniors are in the class?
A. 7
B. 8
C. 9
D. 10
E. 11
A. 7
B. 8
C. 9
D. 10
E. 11
APPROACH #1: Reasoning
If all 17 students were SENIORS, then the number of reports written = (17)(3) = 51
We are told that 44 (not 51) reports were written.
51 - 44 = 7
So, we've accounted for 1 EXTRA book reports.
Each JUNIOR wrote 1 less book report than each senior wrote.
So, there must be 7 juniors.
Answer: A
APPROACH #2: Algebraic
In a certain history class of 17 juniors and seniors...
Since the question asks us to find the number of juniors, let's let x = the number of juniors in the class
Since there are only juniors and seniors, and since there are 17 students in total, we know that 17 - x = the number of seniors in the class
Each junior has written 2 book reports and each senior has written 3 book reports. The 17 students have written a total of 44 book reports
Total number of books written by juniors = 2x
Total number of books written by seniors = 3(17 - x)
So we can write: 2x + 3(17 - x) = 44
Expand: 2x + 51 - 3x = 44
Simplify: -x + 51 = 44
Solve: x = 7
Answer: A
Cheers,
Brent
