A business has two loans totaling $85,000. One loan has a rate of 4.5% and the other has a rate of 6%. This year, the business expects to pay $4,650 in interest on the two loans. How much is each loan?

Answer: Loan a:$30,000, Loan b:$55,000

Step-by-step explanation:

We have to loans, loan a and loan b, and both sum to $85,000:

a + b=$85,000 (1)

On the other hand, we know loan a has a rate of 4.5%=0.045 and loan b has a rate of 6%=0.06:

0.045 a + 0.06 b=$4,650 (2)

So, we have a system with two equations to solve:

Isolating a from (1):

a=$85,000 - b (3)

Substituting (3) in (2):

0.045 ($85,000 - b) + 0.06 b=$4,650 (4)

b=$55,000 (5) This is loan b

Substituting (5) in (1):

a + $55,000=$85,000 (6)

a = $30,000 (7) This is loan a