Question

Gina Chuez has considered starting her own custom greeting card business. With an initial start up cost of $1500, she figures it will cost $0.45 to produce each card. In order to remain competitive with the larger greeting card companies, Gina must sell her cards for no more than $1.70 each. To make a profit, her income must exceed her costs. Determine the number of cards she must sell before making a profit.

Answer 1

1500 + 0.45x < 1.70x
1500 < 1.70x - 0.45x
1500 < 1.25x
1500/1.25 < x
1200 < x.....so she would have to sell 1201 cards to make a profit

Answer 2

The more she charges for her cards, the fewer cards she'll have to sell 
to recover her start-up costs.  So naturally, she wants to charge as much 
for each card as she can get away with. 

Let's start out assuming she charges the maximum of $1.70 for each one 
(and that there are customers willing to pay $1.70 to buy one.) 

It costs Gina $0.45 to produce a card, and she sells it for $1.70.
Her profit from selling each card is    ($1.70 - $0.45)  =  $1.25 profit.

How many times does she need $1.25 in profit to get back the $1500 
that she sank into the business to get it started ?

                 ($1500) / ($1.25 per card)  =  1,200 cards .

That's the minimum number she must sell, and it only works if she 
charges the full $1.70 for each card.  If she charges a lower price 
for them, then she'll need to sell more cards to make up the $1500 .