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XYZ Dentistry produces dental floss. The cost of producing dental floss varies inversely with the number of units produced. When 8,000 floss units are produced, the cost is $0.50 per floss unit. What is the cost per floss unit if XYZ Dentistry produces 25,000 dental floss units?

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sqdancefan

Answer:

  $0.16 per floss unit

Step-by-step explanation:

You want the cost per floss unit for 25000 units if the cost varies inversely with units produced and 8000 units are produced for $0.50 per unit.

Inverse variation

The number of units is increased by a factor of 25000/8000, or 25/8. If the cost is inversely proportional, it will be reduced by the factor 8/25:

  ($0.50/unit) × 8/25 = $0.16/unit

The cost is $0.16 per floss unit if 25,000 units are produced.

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Additional comment

The inverse variation means ...

  (cost/unit) × units = constant

That is, the cost of floss unit production is $4000, regardless of the number of units produced.

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