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------------------------------------------------ Maria and Curtis both study a second language. Maria studies German for 3 hours per week, and Curtis studies French for 2 hours per week. Curtis has already studied for 4 hours when Maria begins her studying. After how many weeks will they have studied the same number of hours?

After setting up an equation based on the hours Maria and Curtis study their second languages, it is determined that after 4 weeks, they will have studied the same number of hours.

Explanation:

We need to find out after how many weeks Maria and Curtis will have studied the same number of hours for their respective languages, German and French.

Maria studies German for 3 hours per week, and Curtis studies French for 2 hours per week. Curtis has a head start with 4 hours already studied before Maria starts.

Let's define 'x' as the number of weeks they both study for. We can set up an equation based on the given information:

Maria's total hours: 3x hours
Curtis's total hours: 2x + 4 hours

To find out when they have studied the same number of hours, we set Maria’s total hours equal to Curtis’s total hours:

3x = 2x + 4

Solving the equation for 'x' we get:

3x = 2x + 4
3x - 2x = 4
x = 4

So, after 4 weeks, they will have studied the same number of hours.