The kerns pen company makes ballpoint pens. the fixed cost of operation for one month averages $53500. the cost of producing one pen is $.75 and the pens are sold for $1.05 each. how many pens must be sold in order for the oay to break even?

  178,334 pens

Step-by-step explanation:

The company makes $0.30 above the variable cost on each pen, so must sell $53,500/$0.30 ≈ 178,334 pens to cover the cost of operation.

Sale of 178,333 pens will result in a total cost of $0.10, so doesn't quite make the company break even. Sale of 178,334 pens will result in profit of $0.20.

These triangles are similar by the AA Similarity Theorem. The triangles share an angle, which makes the two similar. In addition, the created angles (which come from the parallel lines), forces all of the angles to be congruent, while allowing sides to vary in length.

:)