Explain identities and no solutions

9514 1404 393

  97

Step-by-step explanation:

We want to find x when C = 23.

  23 = 0.005x^2 -0.35x +10

  2600 = x^2 -70x . . . . . . subtract 10, multiply by 200

  2600 +35^2 = (x -35)^2 . . . . complete the square

  61.847 +35 = x . . . . . . . square root, add 35 (use the positive result only)

  x ≈ 97 . . . . rounded to integer

The cost is $23 when 97 coolers are produced.