Which inequality models this problem?
Eduardo started a business selling sporting goods. He spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. He earns $850 per week in sales.
What is the minimum number of weeks it will take for Eduardo to make a profit?
A. 300w>7500+850w
B. 850w>7500+300w
C. 850w≥7500+300w
D. 850w<7500+300w
he makes $550 per week ($850 - 300)
how many weeks before recoups the merchandise cost?
To determine the minimum number of weeks it will take for Eduardo to make a profit, we need to consider his expenses and earnings.
Let's break down the problem step by step:
1. Eduardo spent $7500 to obtain his merchandise.
2. He has a weekly expense of $300 for general expenses.
3. He earns $850 per week in sales.
To determine when Eduardo will make a profit, we need to subtract his expenses from his earnings and find when the result is positive.
Let's set up an inequality to represent this situation:
Profit = Earnings - Expenses
Profit = 850w - (7500 + 300w)
where w is the number of weeks.
Simplifying the equation:
Profit = 850w - 7500 - 300w
Profit = 550w - 7500
Now, we need to find when the profit is greater than or equal to zero (to indicate when Eduardo starts making a profit).
550w - 7500 ≥ 0
Adding 7500 to both sides:
550w ≥ 7500
Now, dividing both sides by 550:
w ≥ 7500 / 550
Simplifying further:
w ≥ 13.64
So, the minimum number of weeks it will take for Eduardo to make a profit is approximately 13.64 weeks.
To determine which inequality model represents this problem, we need to find an inequality that matches the derived inequality w ≥ 13.64.
Among the given options, the correct answer is:
C. 850w ≥ 7500 + 300w