SOLUTION: There are three times as many people in the psychology class as in the art history class there are 13 more people in the algebra class then in the heart history class the total enr

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Question 1079325: There are three times as many people in the psychology class as in the art history class there are 13 more people in the algebra class then in the heart history class the total enrollment of the three classes is 78 students how many students are enrolled in each class
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number in psych class
Let +b+ = number in art history class
Let +c+ = number in algebra class
-------------------------------------
(1)
+a+=+3b+
(2)
+c+=+b+%2B+13+
(3)
+a+%2B+b+%2B+c+=+78+
-----------------------
Substitute (1) and (2) into (3)
+a+%2B+b+%2B+c+=+78+
+3b+%2B+b+%2B+b+%2B+13+=+78+
+5b+%2B+13+=+78+
+5b+=+65+
+b+=+13+
and
+a+=+3b+
+a+=+3%2A13+
+a+=+39+
and
+c+=+b+%2B+13+
+c+=+13+%2B+13+
+c+=+26+
---------------------
There are 39 in psych class
There are 13 in art history class
There are 26 in algebra class
-----------------------------
check:
+a+%2B+b+%2B+c+=+78+
+39+%2B+13+%2B+26+=+78+
+78+=+78+