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 earned $850 per week in sales. What is the minimum number of weeks it will take for Eduardo to make a profit? Write an inequality to model the problem.
850x > 300x + 7500
850x - 300x > 7500
550x > 7500
X > 13.6 Weeks.
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To find the minimum number of weeks it will take for Eduardo to make a profit, we need to determine when his total earnings will exceed his total expenses.
Let's denote the number of weeks as "x".
Given that Eduardo spends $300 per week on general expenses, his total expenses in "x" weeks would be 300x.
Since he spent $7500 initially to obtain his merchandise, his total expenses would be 7500 + 300x.
Eduardo earns $850 per week in sales. Therefore, his total earnings in "x" weeks would be 850x.
To determine when Eduardo will make a profit, we need to find the value of x when his total earnings exceed his total expenses. This can be represented by the following inequality:
850x > 7500 + 300x
Simplifying the inequality:
850x - 300x > 7500
550x > 7500
Dividing both sides of the inequality by 550:
x > 7500 / 550
x > 13.64 (rounded to 2 decimal places)
Since we cannot have a fraction of a week, the minimum number of weeks it will take for Eduardo to make a profit is 14 weeks.