1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Allisa [31]
3 years ago
10

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?
Mathematics
1 answer:
lianna [129]3 years ago
8 0

Answer:

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),

C=\frac{22A}{9}+\frac{7000}{3}

Substitute into (I)

A+B+\frac{22A}{9}+\frac{7000}{3}=78000

\frac{31A}{9}+B=78000-\frac{7000}{3}

\frac{31A}{9}+B=\frac{227000}{3}

\frac{31A+9B}{9}=\frac{227000}{3}

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=\frac{22A}{9}+\frac{7000}{3}

C=\frac{22X15000}{9}+\frac{7000}{3} =39000

C=$39000

from (I)

A+B+C=78000

15000+B+39000=78000

B=$24000

You might be interested in
1. If x is the supplementary angle of 155°,
ValentinkaMS [17]

Answer:

0.466 degree is the. answer

6 0
3 years ago
Hi need help on a test for math
enyata [817]

Answer:

i rlly dont want to make you wrong cause i feel lik im wrong but i got all of them as cant be sides of triangles

Step-by-step explanation:

i did use a calculator tho

5 0
3 years ago
Find the missing side lengths​
Effectus [21]
N= 15
M= 15 √ 3
Brainliest please
7 0
3 years ago
HELP<br> Find the area of the polygon with the vertices of A(2,2), B(2,7), C(8,7),and D(4,2)
Illusion [34]

I think it would be 36 it’s what my friend told me I’m not sure though sorry if it’s wrong.

8 0
3 years ago
Which statement is true of an appropriate sample of a population?
Ulleksa [173]
The first statement!
4 0
3 years ago
Read 2 more answers
Other questions:
  • F(x) = -3x^2 -5<br> g(x) = 2x -5 <br><br> Find f(2) x g(6)
    14·1 answer
  • What is the speed of a wave if the wavelength is 100 m and the period is 20 seconds?
    9·2 answers
  • What is the surface area of the sphere
    13·1 answer
  • The Catalog Store has data indicating that, when the price of a CD bookcase is $137, the demand quantity is 56 and the supply qu
    9·1 answer
  • A health survey determined the mean weight of a sample of 762 men between the ages of 26 and 31 to be 173 pounds, while the mean
    11·1 answer
  • Please help me out it would be greatly appreciated
    6·1 answer
  • How to show work 120÷10
    5·2 answers
  • Because you want to prepare and serve the healthiest food possible you monitor the fat and calorie continent of items on your me
    5·1 answer
  • Use the side-splitter theorem to solve for x in the triangle below.
    11·1 answer
  • SOMEONE HELP ME PLEASE
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!