Zach borrowed $50,000 to buy a car, put a down payment on a house, and pay for student loans. Some of the money was borrowed at 5%, some at 6% and some at 7%. How much was borrowed at each rate if the annual interest owed was $3,150 and the amount borrowed at 5% was three times the amount borrowed at 6%?

Question

Zach borrowed $50,000 to buy a car, put a down payment on a house, and pay for student loans. Some of the money was borrowed at 5%, some at 6% and some at 7%. How much was borrowed at each rate if the annual interest owed was $3,150 and the amount borrowed at 5% was three times the amount borrowed at 6%?

Thank you

Answer 1

amount borrowed at 6% ---- x

amount borrowed at 5% = 3x
amount borrowed at 7% = 50000 - 4x

solve for x

.06x + .05(3x) + .07(50000-4x) = 3150
times 100
6x + 15x + 7(50000-4x) = 315000
take over.

Answer 2

To solve this problem, let's set up equations to represent the given information.

Let's denote the amount borrowed at 5% as "x".

According to the problem, the amount borrowed at 5% was three times the amount borrowed at 6%. Therefore, the amount borrowed at 6% is x/3.

The remaining amount borrowed, which is not given in the problem, can be denoted as the difference between the total borrowed amount ($50,000) and the sum of the amounts borrowed at 5% and 6%. So the amount borrowed at 7% is:

$50,000 - (x + x/3)

Now, we'll calculate the interest on each part borrowed at different interest rates.

The interest on the amount borrowed at 5% is 5% of x, which is 0.05x.
The interest on the amount borrowed at 6% is 6% of x/3, which is 0.06(x/3).
The interest on the amount borrowed at 7% is 7% of ($50,000 - (x + x/3)), which is 0.07($50,000 - (x + x/3)).

According to the problem, the total annual interest owed is $3,150. So, we can set up the following equation:

0.05x + 0.06(x/3) + 0.07($50,000 - (x + x/3)) = $3,150

We can now solve this equation to determine the value of x.