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?
Accepted Solution
A:
Answer: Loan a:$30,000, Loan b:$55,000Step-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 bSubstituting (5) in (1):a + $55,000=$85,000 (6)a =$30,000 (7) This is loan a