Question

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?

Answer 1

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.