Question

You are manager of the sweatshirt department at Trends,a clothing manufacturer. Trends plans to produce 25,000 sweatshirts. The Sweatshirts will be sold to stores for $16 each. The cost of manufacturing and marketing each sweatshirt is $10.How many sweatshirts need to be sold for the company to break even? Write an equation using x for the unknown that could be used to solve this problem.

Answer 1

Answer: 15,625 sweatshirts.

Explanation:

Assume that the number of sweatshirts Trends needs to sell to break even is x

- The cost to produce and promote one sweatshirt is $10

=> The cost to produce and promote 25,000 sweatshirts would be:

           $10 x 25,000 = $250,000

- The price of each Sweatshirt at store is $16

=> The revenue Trends generates when selling x sweatshirts is: 16x

- At break even point, the cost to produce and promote 25,000 sweatshirts is equal to the revenue Trends generates when selling x sweatshirts

=> 16x = $250,000

=> x = 250,000 : 16 = 15,625

Conclusion: 15,625 sweatshirts need to be sold for Trends to break even.