Final answer:
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.