SOLUTION: it costs a company $30 to produce 2 widgets,$118 to produce 4 widgets,$766 to produce 10 widgets.how much does it cost to produce 6 widgets?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: it costs a company $30 to produce 2 widgets,$118 to produce 4 widgets,$766 to produce 10 widgets.how much does it cost to produce 6 widgets?      Log On


   

Question 463543: it costs a company $30 to produce 2 widgets,$118 to produce 4 widgets,$766 to produce 10 widgets.how much does it cost to produce 6 widgets?
Answer by lwsshak3(11628) About Me  (Show Source):
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it costs a company $30 to produce 2 widgets,$118 to produce 4 widgets,$766 to produce 10 widgets.how much does it cost to produce 6 widgets?
...
f(x)=Ax^2+Bx+C
3 points to work with (2,30), (4,118), (10,766)
1) 4A+2B+C=30
2) 16A+4B+C=118
3) 100A+10B+C=766
..
2) 16A+4B+C=118
1) 4A+2B+C=30
subtract
4) 12A+2B=88
..
3) 100A+10B+C=766
2) 16A+4B+C=118
subtract
5) 84A+6B=648
6) 36A+6B=264 (multiply eq 4 by 3
subtract
7) 48A=384
A=384/48=8
..
6B=264-36*A (from eq 6)
6B=264-288=-24
B=-24/6=-4
..
C=118-16A-4B (from eq 2)
C=118-128+16=6
..
Equation:
f(x)= 8x^2-4x+6
f(6)=8*36-4*6+6
f(6)=288-24+6=270
..
Ans:
It will cost $270 to make 6 widgets