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. how many cards must she sell before making a profit?

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 .