SOLUTION: When bottles of water cost $.80 per bottle at softball games, 200 bottles were sold. When the price was raised to $1.00 per bottle, only 150 bottles were sold. Determine the number

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: When bottles of water cost $.80 per bottle at softball games, 200 bottles were sold. When the price was raised to $1.00 per bottle, only 150 bottles were sold. Determine the number      Log On


   

Question 1062666: When bottles of water cost $.80 per bottle at softball games, 200 bottles were sold. When the price was raised to $1.00 per bottle, only 150 bottles were sold. Determine the number of bottles of water sold if the price was $.90 per bottle.

Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find the line containing the two points, (0.8, 200), and (1, 150). What is y when x=0.9 ?


y-150=%28%28150-200%29%2F%281-0.8%29%29%28x-1%29

y-150=%28-50%2F0.2%29%28x-1%29

y-150=-250x%2B250

highlight%28y=-250x%2B400%29
now let x=0.9 and find y.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is an inverse linear relation ( I assume ) between
price of bottles and number of bottles sold
You are given 2 points on the line:
( 200, .8 ) and
( 150, 1 )
----------------------
Let +n+ = number of bottles sold
Let +p+ = price/bottle for +n+ bottles sold
-------------------------------------------------
Use the point-slope formula
+%28+p+-+.8+%29+%2F+%28+n+-+200+%29+=+%28+1+-+.8+%29+%2F+%28+150+-+200+%29+
+%28+p+-+.8+%29+%2F+%28+n+-+200+%29+=+.2+%2F+%28-50+%29+
Multiply both sides by +%28+n+-+200+%29%2A%28+-50+%29+
+%28+-50+%29%2A%28+p+-+.8+%29+=+.2%2A%28+n+-+200+%29+
+-50p+%2B+40+=+.2n+-+40+
+-50p+=+.2n+-+80+
Multiply both sides by +-1+
+50p+=+-.2n+%2B+80+
+p+=+-+.004n+%2B+1.6+
-----------------------------
If +p+=+.9+
+.9+=+-.004n+%2B+1.6+
+.004n+=+.7+
+n+=+175+
175 bottles will be sold at $.90/bottle
-----------------------------------
check:
Does the equation go through ( 200, .8 ) ?
+p+=+-+.004n+%2B+1.6+
+.8+=+-+.004%2A200+%2B+1.6+
+.8+=+-.8+%2B+1.6+
+.8+=+.8+
OK
Does the equation go through ( 150,1 ) ?
+p+=+-+.004n+%2B+1.6+
+1+=+-+.004%2A150+%2B+1.6+
+1+=+-+.6+%2B+1.6+
+1+=+1+
OK