SOLUTION: The linear profit equation for a company that sells plastic airtight containers is P=a+bx, where P is the profit in Rands, x is the number of units sold,a and b are constants. When

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The linear profit equation for a company that sells plastic airtight containers is P=a+bx, where P is the profit in Rands, x is the number of units sold,a and b are constants. When      Log On


   

Question 947378: The linear profit equation for a company that sells plastic airtight containers is P=a+bx, where P is the profit in Rands, x is the number of units sold,a and b are constants. When 100 units are sold, the profit is R 21 000 and when 450 units are sold, the profit is R 126 000.
Determine the values of a and b
Draw a neat graph showing profit as a function of the number of units sold.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+a+%2B+b%2Ax+
----------------
(1) +21000+=+a+%2B+b%2A100+
(2) +126000+=+a+%2B+b%2A450+
--------------------------
Subtract (1) from (2)
(2) +126000+=+a+%2B+b%2A450+
(1) +-21000+=+-a+-+b%2A100+
----------------------------
+105000+=+350b+
+b+=+300+
and
(1) +21000+=+a+%2B+b%2A100+
(2) +21000+=+a+%2B+300%2A100+
(2) +a+=+21000+-+30000+
(2) +a+=+-9000+
---------------------------
The equation is:
+P+=+-9000+%2B+300x+
-----------------------
check:
When 450 units are sold, the profit is R 126 000
+126000+=+-9000+%2B+300%2A450+
+126000+=+-9000+%2B+135000+
+126000+=+126000+
----------------------
Here's a plot:
+graph%28+500%2C+500%2C+-100%2C+600%2C+-50%2C+200%2C+-9+%2B+.3x+%29+
This graph has units on both axes scaled down
by a factor of +1000+, so a +K+ has to be
added to all the scale numbers. The equation
on this graph actually looks like: +P+=+-9+%2B+.3x+