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07 Apr 2021, 00:50
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
81% (02:41) correct
19%
(02:58)
wrong
based on 183
sessions
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Originally, the only people in an auditorium were sophomore, juniors, and seniors, and the ratio of sophomores to juniors to seniors was 12 to 18 to 25. After half of the sophomores left the auditorium, a number of juniors equal to the number of juniors originally in the auditorium entered the auditorium, and no one else entered or left the auditorium, the total number of students in the auditorium was 60 more than the original total number of students in the auditorium. What was the original total number of students in the auditorium?
A)275
B)300
C)335
D)350
E)375
A)275
B)300
C)335
D)350
E)375
07 Apr 2021, 01:15
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drithi999
No work required.
The ratio is 12:18:25, so the total should be a multiple of (12+18+25)=55.
All are multiples of 5, but only A is multiple of 11.
A
Method:
The ratio is 12:18:25, so the total = a (12+18+25)=55a, where is the common ratio.
Quote:
So half of 12a left and 18a joined, resulting in additional 60 => \(18a-6a=60......a=5\)
Total = \(55a=55*5=275\)
A
16 Apr 2021, 09:28
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drithi999
Solution:
Originally, there were 12x + 18x + 25x = 55x students in the auditorium, where 12x is the number of sophomores, 18x is the number of juniors, and 25x is the number of seniors.
When half of the 12x sophomores left the auditorium, there were 6x sophomores remaining.
When the same number of juniors as originally present (which was 18x) entered the auditorium, the number of juniors doubled, from 18x to 36x.
The number of seniors did not change from the original 25x.
The new number of students in the auditorium was now 6x + 36x + 25x, and this total was 60 more than the original number of students in the auditorium. Thus, we can create the equation:
6x + 36x + 25x = 55x + 60
67x = 55x + 60
12x = 60
x = 5
Thus, we see that there were (55)(5) = 275 students originally in the auditorium.
Answer: A
