SOLUTION: A used car salesman purchased a number of very old battered cars during the past month. He paid the same price, $89, for each. He has not yet sold all of the cars, but those that h

Algebra ->  Equations -> SOLUTION: A used car salesman purchased a number of very old battered cars during the past month. He paid the same price, $89, for each. He has not yet sold all of the cars, but those that h      Log On


   



Question 1031529: A used car salesman purchased a number of very old battered cars during the past month. He paid the same price, $89, for each. He has not yet sold all of the cars, but those that he has sold went for $225, a piece. He has already made a profit of $2,327 (total sale price minus outlay for all cars purchased). If his car lot has room for no more than 50 cars at one time, how many cars remain?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number of cars he sold
Let +y+ = the number of cars remaining
-----------------------------------
(1) +89%2A%28+x+%2B+y+%29+ = cost of all the cars he bought
(2) +225x+-+89%2A%28+x+%2B+y+%29+=+2327+ profit after selling +x+ cars
(3) +x+%2B+y+%3C=+50+
----------------------
(2) +225x+-+89x+-+89y+=+2327+
(2) +136x+-+89y+=+2327+
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I think I got this by trial and error
First, I divided +2327+%2F+136+=+17.1+
so, +x+ must be at least +17+
Then I tried different value for +x+
+x+=+23+
+23%2A136+=+3128+
+89y+=+3128+-+2327+
+89y+=+801+
+y+=+9+
9 cars remain
-----------------
check:
+x+%2B+y+=+23+%2B+9+
+x+%2B+y+=+32+
(2) +225x+-+89%2A%28+x+%2B+y+%29+=+2327+
(2) +225%2A23+-+89%2A32+=+2327+
(2) +5175+-+2848+=+2327+
(2) +2327+=+2327+
OK
Maybe there is a systematic way to
get the answer -I don't know what it is.
Hope this helps