Algebra Word Problem

Question

Two rival shoe companies want to rent the same empty building for their office and shipping space. Diva's shoes needs 1000 square feet for offices, 600 for shipping, and another 6 square feet for every packaged box of shoes. ShoesRUs needs 750 square feet for offices, 400 for shipping, and 9 square feet per packaged box of shoes. If only one company will fit exactly into the empty building and they both plan to have the same amount of inventory, determine how many boxes of shoes both companies hope to have at any given time. 

 

 

Please explain how to set up and solve the problem. Thank you so much!!

Answer 1

Divas needs 1600 fixed space (1000+600) plus 6 variable space.

Shoes needs 1150 fixed + 9 variable.

 

Since we know they'd be renting the same amount of space, you can now set them equal to each other to solve for the total inventory.

 

1600 + 6x = 1150 + 9x

450 = 3x

150 = x

 

So the companies plan to keep 150 boxes at any given time.