SOLUTION: On Monday Ben took twice as many calls as Alan. Chris took three times as many calls as Ben. Doug took half as many calls as Chris. The total number of calls of the 4 agents added

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Question 1045934: On Monday Ben took twice as many calls as Alan. Chris took three times as many calls as Ben. Doug took half as many calls as Chris. The total number of calls of the 4 agents added together was 480.
How many calls did each agent take?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +b+=+2a+
(2) +c+=+3b+
(3) +d+=+%281%2F2%29%2Ac+
(4) +a+%2B+b+%2B+c+%2B+d+=+480+
---------------------------
(2) +c+=+3%2A%282a%29+
(2) +c+=+6a+
and
(3) +d+=+%281%2F2%29%2Ac+
(3) +d+=+%281%2F2%29%2A6a+
(3) +d+=+3a+
----------------------
Substitute these results into (4)
(4) +a+%2B+b+%2B+c+%2B+d+=+480+
(4) +a+%2B+2a+%2B+6a+%2B+3a+=+480+
(4) +12a+=+480+
(4) +a+=+40+
and
(1) +b+=+2a+
(1) +b+=+2%2A40+
(1) +b+=+80+
and
(2) +c+=+6a+
(2) +c+=+6%2A40+
(2) +c+=+240+
and
(3) +d+=+3a+
(3) +d+=+3%2A40+
(3) +d+=+120+
Alan made 40 calls
Ben made 80 calls
Chris made 240 calls
Doug made 120 calls
----------------------
check:
(4) +a+%2B+b+%2B+c+%2B+d+=+480+
(4) +40+%2B+80+%2B+240+%2B+120+=+480+
(4) +480+=+480+
OK