A customer purchased a car and financed $16,000. The customer borrowed part of the money from a bank charging 10% annual interest and the rest from a credit union at 8% annual interest. If the total interest for the year was $1,390 how much was borrowed from the bank and how much was borrowed from the credit union?

Question

A customer purchased a car and financed $16,000. The customer borrowed part of the money from a bank charging 10% annual interest and the rest from a credit union at 8% annual interest. If the total interest for the year was $1,390 how much was borrowed from the bank and how much was borrowed from the credit union?

Answer 1

Set this up as an algebra problem in two variables. Let X be borrowed at 10% and Y be borrowed at 8%. Here is what you know:

X + Y = 16,000
0.10X + 0.08Y = 1390

Solve by substitution, or by multiplying the second equation by 10 and subtracting from the first.

X + 0.8Y = 13900
0.2Y = 2100
Y = 10,500

Now solve for X. It is the rest of the $16,000.

Answer 2

To find out how much was borrowed from the bank and the credit union, we can start by setting up a system of equations based on the given information.

Let's assume the amount borrowed from the bank is x dollars and the amount borrowed from the credit union is y dollars.

From the given information, we know that the total amount financed is $16,000. So, we can write our first equation:

x + y = 16,000 ...(equation 1)

We are also given that the total interest for the year was $1,390. The interest from the bank can be calculated using the formula: Interest = Principal * Rate. Similarly, the interest from the credit union can be calculated using the same formula.

The interest from the bank will be: 0.10 * x ...(equation 2)
The interest from the credit union will be: 0.08 * y ...(equation 3)

Now, we can write our second equation based on the total interest:

0.10x + 0.08y = 1,390 ...(equation 4)

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method:

From equation 1, we can rewrite it as: y = 16,000 - x.

Now substitute this value of y in equation 4:

0.10x + 0.08(16,000 - x) = 1,390

Simplify and solve for x:

0.10x + 1,280 - 0.08x = 1,390
0.02x = 1,390 - 1,280
0.02x = 110

Divide both sides by 0.02:

x = 110 / 0.02
x = 5,500

So, $5,500 was borrowed from the bank.

To find out how much was borrowed from the credit union, substitute the value of x in equation 1:

y = 16,000 - x
y = 16,000 - 5,500
y = 10,500

Therefore, $10,500 was borrowed from the credit union.

In summary, $5,500 was borrowed from the bank and $10,500 was borrowed from the credit union.