Erin has developed a new lotion that will children with sensitive skin. she invests $15,225 in equipment to manufacture and package her lotion. each bottle costs $3.25 to manufacture and sells for $12. how many bottles of lotion must she make and sell before her business breaks even?

"Break even" occurs when Revenue = Costs.

So, solve this equation:  

                                       ($12/bottle)x = $15225 + ($3.25)x

Consolidating the x terms:  $8.75x = $15225
                                                            $15225
Solving for x:                                x = = 1740 bottles
                                                                $8.75

Her business will break even when she has sold 1740 bottles of her lotion.