Answer:
Federal student loans (F): $6,000
Private bank loans (P): $54,000
Explanation:
Let's denote the amount of the federal student loans as F and the amount of the private bank loans as P.
From the given information, we have two equations:
Josie owes a total of $60,000 in student loans:
F + P = $60,000
The total interest she owes for one year is $2,760, and we know the interest rates for both federal and private loans:
0.028F + 0.048P = $2,760
Now, we can solve this system of linear equations. We can start by solving the first equation for one of the variables and then substitute it into the second equation:
From the first equation, we can express F in terms of P:
F = $60,000 - P
Now, substitute this expression for F into the second equation:
0.028($60,000 - P) + 0.048P = $2,760
Now, let's solve for P:
0.028($60,000) - 0.028P + 0.048P = $2,760
1,680 - 0.028P + 0.048P = $2,760
Combine the like terms:
0.02P = $2,760 - $1,680
0.02P = $1,080
Now, divide by 0.02 to isolate P:
P = $1,080 / 0.02
P = $54,000
So, the amount of the private bank loans (P) is $54,000.
Now, we can find the amount of federal student loans (F) using the first equation:
F + $54,000 = $60,000
F = $60,000 - $54,000
F = $6,000
So, the amount of the federal student loans (F) is $6,000.
To summarize:
Federal student loans (F): $6,000
Private bank loans (P): $54,000