## Chelsea took out three loans for a total of ​$78 comma 000 78,000 to start an organic orchard. Her​ business-equipment loan was at an inter Question Chelsea took out three loans for a total of ​$ 78 comma 000 78,000 to start an organic orchard. Her​ business-equipment loan was at an interest rate of​ 11%, the​ small-business loan was at an interest rate of 5 5​%, and her​ home-equity loan was at an interest rate of 4.5 4.5​%. The total simple interest due on the loans in one year was ​$4605 4605. The annual simple interest on the​ home-equity loan was ​$ 105 105 more than the interest on the​ business-equipment loan. How much did she borrow from each​ source?

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1 week 2021-09-14T06:46:48+00:00 1 Answer 0

Business-equipment loan, A=$15000 Small-business loan, B=$24000

home-equity loan, C= $39000 Step-by-step explanation: Let the Business-equipment loan at an interest rate of​ 11%=A Let the​ small-business loan was at an interest rate of 5​% =B Let her​ home-equity loan was at an interest rate of 4.5​%.=C Since her total Loan=$78000

A+B+C=78000….(I)

Simple Interest = (P X R X T)/100

Since the Time, T=1 year

Interest on A = 0.11A

Interest on B = 0.05B

Interest on C = 0.045C

The total simple interest due on the loans in one year was ​$4605. 0.11A+0.05B+0.045C=4605….(II) The annual simple interest on the​ home-equity loan was ​$105 more than the interest on the​ business-equipment loan.

0.045C = 0.11A +105…(III)

We proceed to solve the simultaneous equations.

A+B+C=78000….(I)

0.11A+0.05B+0.045C=4605….(II)

0.045C = 0.11A +105…(III)

From (III), 0.045C = 0.11A +105

Substitute 0.045C = 0.11A +105 into (II).

0.11A+0.05B+0.11A +105=4605

0.22A+0.05B=4500

From (III), Substitute into (I)    3(31A+9B)=9 X 227000

31A+9B=681000

0.22A+0.05B=4500 (Multiply by 9)

31A+9B=681000 (Multiply by 0.05)

1.98A+0.45B=40500

1.55A+0.45B=34050

Subtracting

0.43A=6450

A=$15000 From (III)  C=$39000

from (I)

A+B+C=78000

15000+B+39000=78000

B=\$24000