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
Steven has some money. If he spends $9.00, then he will have 3 5of the amount he started with
docker41 [41]
$1.80 if the question was ( he would have 3/5 of the amount he started with)
7 0
2 years ago
Can someone sub to my youttube channel pls, its called Yakobu, it would really help out :)
mestny [16]

Answer:

yea i will what do u do ther???

Step-by-step explanation:

ohhhh gamer

6 0
3 years ago
There are two numbers such that , if both of them are individually increased by 5 and then by the same percentage as they were i
QveST [7]
Let the two numbers be x and y.
Let m =  the fraction (or percentage) for increasing the numbers.
 
Increase x by 5, multiply (x+5) by (1+m), and set it qual to 36.
(x + 5)*(1 + m) = 36

Increase y by 5, multiply (y+5) by (1+m), and set it equal to 36.
(y+5)*(1+m) = 36

Therefore
(x+5)*(1+m) = (y+5)*(1+m)
x + 5 = y + 5
x = y
x - y = 0

Answer: 0.
The difference between the two numbers is zero.
5 0
3 years ago
The quantity of 6 less than a number multiplied by 8
Bas_tet [7]

6x-6=8x

subtract 6x from both sides

-6=2x

divide both sides by 2

x= -3

5 0
3 years ago
What is 28 and 29 plz help
PtichkaEL [24]
28 is False
29 is True

~Hope this helped~
7 0
3 years ago
Read 2 more answers
Other questions:
  • Leena knits 10 rows in 12 min. At this pace, how long will it take her to knit the next 25 rows? Enter your answer in the box.
    14·2 answers
  • The midpoint between two points is( 1 , 5 ). One of those points is ( 9 , 3 ), find the other. DUE in 2 HOURS, will give Brainli
    11·2 answers
  • A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller. W
    11·2 answers
  • Which relations are functions? Select function or not a function for each graph
    12·1 answer
  • Charlie runs at a speed of 3 yards per second . About how many miles per hour does Charlie run?
    6·1 answer
  • Problem Page
    5·1 answer
  • Does - 3/4 + 3/5 have a positive, negative or zero sum?
    9·2 answers
  • A triangle has sides with lengths of 4 meters, 5 meters and 3 meters . Is it a right triangle? ​
    13·1 answer
  • Anyone know the answer will give brainliest if correct.
    9·2 answers
  • Here is another one <br> 5. 1 4/5 × 15
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!