Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her S200 per week for general expenses. She earns $550 per week in sales. What is the minimum number of weeks it will take to make a profit?

1 Answer
Nov 29, 2016

Answer:

It will be a minimum of 13 weeks before Josephine makes a profit.

Explanation:

To solve this problem we need to determine how many weeks (let's call this #w#) it will take Josephine's sales to exceed her up front and ongoing weekly costs.

We can represent her weekly sales over #w# weeks as #$550*w#

And we can represent her up front and weekly costs over #w# weeks as: $4500 + $200w#.

Now, we need to know when:

#$550w - ($4500 + $200w) > 0#

Solving for #w# gives:

#550w - 4500 - 200w > 0#

#(550 - 200)w - 4500 > 0#

#350w - 4500 > 0 #

#350w - 4500 + 4500 > 0 + 4500#

#350w > 4500#

#(350w)/350 > 4500/350#

#w > 12.9# rounded to the nearest tenth.