SOLUTION: At the north campus, 5% of the students in the department are men. At the south campus, 80% of the students in the department are men. After the merger, 50% of the 150 students ar

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: At the north campus, 5% of the students in the department are men. At the south campus, 80% of the students in the department are men. After the merger, 50% of the 150 students ar      Log On


   



Question 962125: At the north campus, 5% of the students in the department are men. At the south campus, 80% of the students in the department are men. After the merger, 50% of the 150 students are men. How many students were in the department at the north and south campuses before the merger?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of men on N.C.
Let +b+ = number of men on S.C.
--------------------------------
(1) +a+%2B+b+=+150+
(2) +.05a+%2B+.8b+=+.5%2A150+
---------------------------
(2) +.05a+%2B+.8b+=+75+
(2) +5a+%2B+80b+=+7500+
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5a+%2B+80b+=+7500+
(1) +-5a+-+5b+=+-750+
-------------------------
+75b+=+6750+
+b+=+90+
and
(1) +a+%2B+b+=+150+
(1) +a+=+150+-+90+
(1) +a+=+60+
----------------
There were 60 men on N.C.
There were 90 men on S.C.
check:
(2) +.05a+%2B+.8b+=+75+
(2) +.05%2A60+%2B+.8%2A90+=+75+
(2) +3+%2B+72+=+75+
(2) +75+=+75+
OK