SOLUTION: Jania sells scarves for $12 each through Etsy.com, a site where people can sell homemade items. Each scarve costs Jania $5.70 to make. Jania had to pay a one-time fee to Etsy of $1

Question 934128: Jania sells scarves for $12 each through Etsy.com, a site where people can sell homemade items. Each scarve costs Jania $5.70 to make. Jania had to pay a one-time fee to Etsy of $150 to put her items on the website. Jania wants to make sure she can turn a profit on her scarves so she can buy Christmas gifts for the holidays and asks for help. My job is to inform Jania on making a profit on her scarves.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
profit = revenue minus cost.
let x = number of scarves she sells.
revenue = 12x
cost = 5.7x + 150
profit = revenue minus cost becomes profit = 12x minus (5.70x + 150.
this can be simplified to profit = 12x - 5.70x - 150.
this can be further simplified to profit = 6.3x - 150.
if she knows how much profit she needs to make, she can use this equation to determine how many scarves she needs to sell.
she can also use this equation to determine when she breaks even.
she breaks even when her profit is 0.
profit - 6.3x - 150 becomes 0 = 6.3x - 150
solve for x to get x = 23.8....
she will break even and make a small profit when she sells 24 scarves.
6.3*24 - 150 = 151.2 - 150 = 1.2 dollars.
every scarf she sells over 24 will net her a profit of 6.3 dollars in addition to the 1.2 dollars.
this is because her fixed cost has been satisfied (the 150 dollars) and the only thing left is her incremental cost (the 5.70 per scarf).

RELATED QUESTIONS
Jania sells scarves for $12 each through Etsy.com, a site where people can sell homemade... (answered by josgarithmetic)

Jania sells scarves for $12 each through Etsy.com, a site where people can sell homemade... (answered by josgarithmetic)

A student knits scarfs and sells them at craft shows. The yarn to make each scarf costs... (answered by addingup)

you are buying scarves and gloves as gifts. a scarf costs $2 less than each pair of... (answered by nerdybill,ewatrrr)

Jean goes to a movie theater where a ticket costs $7 and any snack item-candy,popcorn,or... (answered by ankor@dixie-net.com)

Troy makes fleece scarves and sells them for $8 each. The supplies cost him $2 per... (answered by josgarithmetic,MathTherapy)

Tiffany makes scarves and sells them at a neighborhood clothing store the owner charges... (answered by jorel555)

Solve the following graphically and algebraically showing your work. Katie makes and... (answered by Boreal)

A machine to make stickers costs 12 dollars and each sheet of paper costs .50 sense each (answered by richwmiller)