Question

Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earns $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit?

Answer 1

Net gain/loss for a week = earn money - spent money, 550-200 = 350

By that amount of profit, it will take, 4500/350 =12.8

So, minimum 13 weeks, it will take for Jose to make a profit.

Answer 2

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

Explanation:

Let it takes w weeks for Josephine to make profit.

So, her weekly sales over 550 is shown as 550w.

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)`

Solving for w:

`550w-200w>4500`

=>
`350w>4500`

w>12.85

Means w should be at least 13.

Hence, It will take a minimum of 13 weeks before Josephine makes a profit.