Question

A student takes out two loans totaling $3000 to help pay for college expenses. One loan is at 8% interest, and the other is at 10% interest. The total amount of interest owed is $264. Find the amount for each loan.

A. Loan 1: $1000, Loan 2: $2000.
B. Loan 1: $1200, Loan 2: $1800.
C. Loan 1: $1400, Loan 2: $1600.
D. Loan 1: $1600, Loan 2: $1400.

Answer 1

Using a system of linear equations with the given interest rates and the total amount of interest, we calculate the sizes of the two loans to be $1800 and $1200, which is option B.

Step-by-step explanation:

To solve the problem of finding the amount for each loan, we can set up a system of linear equations based on the given information. We have two unknowns: let's call the amount of the first loan x and the amount of the second loan y. The total amount borrowed is $3000, so we have the equation:

x + y = 3000

The total interest is $264, which includes interest from both loans. The first loan has an interest rate of 8%, and the second loan has an interest rate of 10%. Therefore:

0.08x + 0.10y = 264

Now we can solve this system of equations simultaneously. To do this, we can multiply the first equation by 0.08 to make subtraction of the equations easier:

0.08x + 0.08y = 240

Subtract this new equation from the second equation:

(0.08x + 0.10y) - (0.08x + 0.08y) = 264 - 240

0.02y = 24

Now divide by 0.02 to get the value for y:

y = 24 / 0.02

y = 1200

Since x + y = 3000, we substitute y = 1200 to find x:

x + 1200 = 3000

x = 3000 - 1200

x = 1800

Therefore, Loan 1 is $1800 and Loan 2 is $1200, which corresponds to option B.