Rocco borrowed a total of $5000 from two student loans. One loan charged 3% simple interest and the other charged 2.5 simple interest, both payable after graduation. If the interest he owed after 1 year was $132.50, determine the amount of principal for each loan.

Let's denote the amount of principal for the first loan as P1 and the amount of principal for the second loan as P2. According to the information provided: The first loan charged 3% simple interest. The second loan charged 2.5% simple interest. The total amount borrowed was $5000. The interest after 1 year was $132.50. We can set up two equations based on the simple interest formula: For the first loan: Interest1 = P1 * (0.03) * 1 year For the second loan: Interest2 = P2 * (0.025) * 1 year Since the total interest after 1 year was $132.50, we can write an equation for the total interest: Total Interest = Interest1 + Interest2 Now, let's substitute the values and equations: $132.50 = P1 * 0.03 * 1 + P2 * 0.025 * 1 Simplify the equations: $132.50 = 0.03P1 + 0.025P2 We also know that the total amount borrowed was $5000, so: Total Principal = P1 + P2 = $5000 Now we have a system of two equations: $132.50 = 0.03P1 + 0.025P2 P1 + P2 = $5000 We can use these equations to solve for P1 and P2. Let's use the second equation to express one of the variables in terms of the other and substitute it into the first equation: P2 = $5000 - P1 Now, substitute this expression for P2 into the first equation: $132.50 = 0.03P1 + 0.025($5000 - P1) Now, simplify and solve for P1: $132.50 = 0.03P1 + $125 - 0.025P1 Combine like terms: $132.50 = 0.005P1 + $125 Subtract $125 from both sides: $132.50 - $125 = 0.005P1 $7.50 = 0.005P1 Now, divide by 0.005 to isolate P1: P1 = $7.50 / 0.005 P1 = $1500 So, Rocco borrowed $1500 for the first loan. Now, we can find the principal for the second loan using the total principal equation: P1 + P2 = $5000 $1500 + P2 = $5000 Subtract $1500 from both sides: P2 = $5000 - $1500 P2 = $3500 Rocco borrowed $1500 for the first loan and $3500 for the second loan.