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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 4 hours when Maria begins to study. After how many weeks will they have studied the same number of hours? Write the system of equations and then solve. Show your work.

A) 3 weeks
B) 4 weeks
C) 5 weeks
D) 6 weeks

Answer :

Final answer:

They will have studied the same number of hours after 4 weeks. Maria studies 3 hours per week while Curtis studies 2 hours per week, with Curtis starting 4 hours ahead. After 4 weeks, Maria will have caught up, totaling 12 hours each.Thus option D is correct.

Explanation:

To solve this problem, we'll create a system of equations representing the hours studied by Maria and Curtis over time. Let ( M ) represent the total hours Maria has studied, and ( C ) represent the total hours Curtis has studied. We know that Maria studies German for 3 hours per week, and Curtis studies French for 2 hours per week. Curtis starts with 4 hours of study before Maria begins.

So, the equations representing their total hours studied over time are:

1.( M = 3w ) (Maria's study hours where ( w ) is the number of weeks)

2. ( C = 2(w - 4) ) (Curtis's study hours, adjusted for the 4 hours he already studied before Maria began)

To find when they've studied the same number of hours, we'll set these equations equal to each other:

( 3w = 2(w - 4) )

Now, solve for ( w ):

( 3w = 2w - 8 )

( w = 8 )

So, they will have studied the same number of hours after 8 weeks, but we need to account for the 4 hours Curtis studied before Maria began. Thus, the answer is ( 8 - 4 = 4 ) weeks. Therefore, the correct answer is option B) 4 weeks.

Thus option D is correct.

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