We may check it with each answer:
In 15 weeks he will earn $850 * 15 = $12 750
In 13 weeks he will earn $850 * 13 = $11 050
In 12 weeks he will earn $850 * 12 = $10 200
In 14 weeks he will earn $850 * 14 = $11 900
Now let's check how much he will spend for general expenses:
In 15 weeks he will spend $300 * 15 = $4 500
In 13 weeks he will spend $300 * 13 = $3 900
In 12 weeks he will spend $300 * 12 = $3 600
In 14 weeks he will spend $300 * 14 = $4 200
Now add $7500 to each option:
15 weeks: $4 500 + $7 500 = $12 000
13 weeks: $3 900 + $7 500 = $11 400
12 weeks: $3 600 + $7 500 = $11 100
14 weeks: $4 200 + $7 500 = $11 700
So:
In 15 weeks he will have expenses of $12 000 and he will earn $12 750
In 13 weeks he will have expenses of $11 400 and he will earn $11 050
In 12 weeks he will have expenses of $11 100 and he will earn $10 200
In 14 weeks he will have expenses of $11 700 and he will earn $11 900
In 12 and 13 weeks Eduardo won't earn enough money to have a profit, but he will obtain it after 14 and more weeks.
Answer: 14 weeks
