Question

A business has two loans totaling $8500. One loan has a rate of 4.5% and the other has a rate of 6%. This year, the business expects to pay $4650 in interest on the two loans. How much is each loan?

a) Loan 1: $3000, Loan 2: $5500

b) Loan 1: $4000, Loan 2: $4500

c) Loan 1: $5000, Loan 2: $3500

d) Loan 1: $3500, Loan 2: $5000

Answer 1

Loan 1 is $5000 and Loan 2 is $3500.

Step-by-step explanation:

Let's assume Loan 1 is x and Loan 2 is y.

We know that the total amount of the loans is $8500, so we can write the equation x + y = 8500.

We also know that the interest paid on Loan 1 (at a rate of 4.5%) plus the interest paid on Loan 2 (at a rate of 6%) equals $4650, so we can write the equation 0.045x + 0.06y = 4650.

To solve this system of equations, we can use substitution or elimination.

Let's use elimination:

Multiply the first equation by -0.06 and the second equation by 0.045 to make the coefficients of y the same:

-0.06x - 0.06y = -0.06(8500)

0.045x + 0.045y = 0.045(4650)

-0.06x - 0.06y = -510

0.045x + 0.045y = 209.25

Add the two equations together:

-0.015y = -300.75

Solve for y:

y = -300.75 / -0.015

y = 20250

Substitute the value of y back into the first equation to solve for x:

x + 20250 = 8500

x = 8500 - 20250

x = -11750

We can see that the negative value for x doesn't make sense in this context, so we can discard it.

Therefore, Loan 1 is $5000 and Loan 2 is $3500.