​Regrind, Inc. regrinds used typewriter platens. The cost per platen is ​$1.10. The fixed cost to run the grinding machine is ​$195 per day. If the company sells the reground platens for ​$6.10​, how many must be reground daily to break​ even?

39

Explanation:

The number that must be reground to break even will be calculated thus:

The total cost for x platens will be:

C(x) = 195 + 1.1x

The total revenue for x platens will be:

R(x) = 6.1x

The equation for breakeven will be:

C(x) = R(x)

195 + 1.1x = 6.1x

6.1x - 1.1x = 195

5.0x = 195

x = 195/5.0

x = 39

To breakeven, 39 must be reground daily.

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