SOLUTION: You need to find a formula for the number of cars produced by a new plant that was opened 25 days ago. You are told that three days ago the plant had 450 cars on hand, and that yes

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You need to find a formula for the number of cars produced by a new plant that was opened 25 days ago. You are told that three days ago the plant had 450 cars on hand, and that yes      Log On


   



Question 951430: You need to find a formula for the number of cars produced by a new plant that was opened 25 days ago. You are told that three days ago the plant had 450 cars on hand, and that yesterday it had 480 cars on hand. You also are told that some of these cars came from previous inventory. Assume that the plant produces cars at this same rate and has produced them at this same rate since it opened.
1) How many cars were on hand when the plant opened?
2) How many cars will be on hand in five days.
3) When will the plant have 720 cars on hand?
4) How many cars were on hand five days ago?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The number of cars produced "depends" on
the number of days the plant is running, so
I can plot Cars Produced, +C+, on the vertical
axis and Days Open +d+ on the horizontal axis.
---------------------
3 days ago was 22 days since plant opened
Yesterday was 24 days since plant opened
Use the general point-slope formula:
+%28+C+-+450+%29+%2F+%28+d+-+22+%29+=+%28+480+-+450+%29+%2F+%28+24+-+22+%29+
+%28+C+-+450+%29+%2F+%28+d+-+22+%29+=+30+%2F+2+
+%28+C+-+450+%29+%2F+%28+d+-+22+%29+=+15+
+C+-+450+=+15%2A%28+d+-+22+%29+
+C+-+450+=+15d+-+330+
+C+=+15d+%2B+120+
-------------------
check:
+d+=+22+
+C+=+15%2A22+%2B+120+
+C+=+330+%2B+120+
+C+=+450+
---------------
+d+=+24+
+C+=+15%2A24+%2B+120+
+C+=+360+%2B+120+
+C+=+480+
-----------------------
(1) When plant opened:
+d+=+0+
+C+=+15%2A0+%2B+120+
+C+=+120+
-----------------------
(2) In +5+ days,
+d+=+25%2B5+=+30+
+C+=+15%2A30+%2B+120+
+C+=+450+%2B+120+
+C+=+570+
---------------------
(3) +C+=+720+
+720+=+15d+%2B+120+
+15d+=+720+-+120+
+15d+=+500+
+d+=+33.333+
( this is during the 34th day )
--------------------------
(4) +d+=+20+
+C+=+15%2A20+%2B+120+
+C+=+300+%2B+120+
+C+=+420+
---------------------
Hope I got it. It's a strange problem
because the plant just keeps filling up
and no cars get shipped ???