Question

Which inequality models this problem? 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? 550w<4500+200w 550w>4500+200w 200w≥4500+550w 200w>4500+500w

Answer 1

550w>4500+200w because she earns 550 per week and spends 200 a week but originally spent 4500 and it has to be a greater than sign not a greater than or equal to sign because she wants to make a profit not just be equal to how much she originally spent.

Answer 2

The correct answer is:

550w>4500+200w

Explanation:

Since she earns $550 per week, Josephine's earnings can be represented as 550w, where w is the number of weeks.

Her costs are $200 per week, or 200w, plus the 4500 start up costs; this gives us 200w+4500.

We want a profit; this means the amount she earns, 550w, must be greater than the costs, 200w+4500:

550w > 200w + 4500, or

550w > 4500 + 200w