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) $1,200 at 8% interest and $1,800 at 10% interest.
B) $1,800 at 8% interest and $1,200 at 10% interest.
C) $1,500 at 8% interest and $1,500 at 10% interest.
D) $2,000 at 8% interest and $1,000 at 10% interest.

Answer 1

The correct amounts for the student's loans are $1,800 at 8% interest and $1,200 at 10% interest, which is Option B. This conclusion is reached by setting up a system of equations and solving for the amount of each loan.

Step-by-step explanation:

The student wants to know the amounts for each loan taken to pay for college expenses. We have two loans totaling $3,000 with differing interest rates and a combined interest owed of $264. We can set up a system of equations to solve this problem.

Let x be the amount of the first loan at an 8% interest rate, so the second loan will be y = $3,000 - x at a 10% interest rate. The equations based on the interest for each loan would be:

• 0.08x = the amount of interest from the first loan
• 0.10($3,000 - x) = the amount of interest from the second loan

These two amounts add up to the total interest:

0.08x + 0.10($3,000 - x) = $264

Now, we solve for x:

0.08x + $300 - 0.10x = $264

-0.02x = $264 - $300

-0.02x = -$36

x = $1,800

Thus, the amount at 8% interest is $1,800, and the remaining $1,200 is at 10% interest since $3,000 - $1,800 = $1,200. The correct answer is Option B: $1,800 at 8% interest and $1,200 at 10% interest.