SOLUTION: Given the cost function C= .25x^2 + 10x +200, fund the number of units x that would have a cost of $2000. Round answer to the nearest unit.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Given the cost function C= .25x^2 + 10x +200, fund the number of units x that would have a cost of $2000. Round answer to the nearest unit.       Log On


   

Question 1046833: Given the cost function C= .25x^2 + 10x +200, fund the number of units x that would have a cost of $2000. Round answer to the nearest unit.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C+=+.25x%5E2+%2B+10x+%2B+200+
+C+=+2000+
+2000+=+.25x%5E2+%2B+10x+%2B+200+
+.25x%5E2+%2B+10x+-+1800+=+0+
+x%5E2+%2B+40x+-+7200+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+40+
+c+=+-7200+
+x+=+%28+-40+%2B-+sqrt%28+40%5E2+-+4%2A1%2A%28-7200%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+-40+%2B-+sqrt%28+1600+%2B+28800+%29%29+%2F+2+
+x+=+%28+-40+%2B-+sqrt%28+30400+%29%29+%2F+2+
+x+=+%28+-40+%2B+174.356+%29+%2F+2+
+x+=+134.356+%2F+2+
+x+=+67.178+
----------------------------
67 units have a cost of $2000
check:
+2000+=+.25x%5E2+%2B+10x+%2B+200+
+2000+=+.25%2A67.178%5E2+%2B+10%2A67.178+%2B+200+
+2000+=+1128.221+%2B+671.78+%2B+200+
+2000+=+2000.001+
OK