SOLUTION: Help on this problem would be greatly appreciated! A village wants to build a community center that is projected to cost 1.2 million dollars. Cost per resident is increased by $3

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Question 637539: Help on this problem would be greatly appreciated!
A village wants to build a community center that is projected to cost 1.2 million dollars. Cost per resident is increased by $3 as it is discovered that there are 225 fewer residents than when planning began 2 years ago. What is the revised cost per resident?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the original number of residents
Let +d+ = the original cost/resident
(1) +1200000+=+d%2An+
(2) +1200000+=+%28+d+%2B+3+%29%2A%28+n+-225+%29+
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(2) +1200000+=+d%2An+%2B+3n+-+225d+%2B+675+
Substitute (1) into (2)
(2) +1200000+=+1200000+%2B+3n+-+225c+%2B+675+
(2) +3n+=+225d+-+675+
(2) +n+=+75d+-+225+
Substitute this back into (1)
(1) +1200000+=+d%2A%28+75c+-225+%29++
(1) +75d%5E2+-+225d+-1200000+
(1) +d%5E2+-+3d+-+16000+
+d+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-3+
+c+=+-16000+
+d+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2+-+4%2A1%2A%28-16000%29+%29%29%2F%282%2A1%29+
+d+=+%28+3+%2B-+sqrt%28+9+%2B+64000+%29%29+%2F+2+
+d+=+%28+3+%2B-+sqrt%28++64009+%29%29+%2F+2+
+d+=+%28+3+%2B+253%29+%2F+2+
+d+=+256%2F2+
+d+=+128+
+d+%2B+3+=+131+
The revised cost/resident is $131
check:
(1) +1200000+=+d%2An+
(1) +n+=+1200000+%2F+128+
(1) +n+=+9375+
and
(2) +1200000+=+%28+128+%2B+3+%29%2A%28+9375+-225+%29+
(2) +1200000+=+131%2A9150+
{2) +1200000+=+1198650+
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This is close but a little off. Can you see where I
messed up?