Maria3737
13.03.2020 •
Mathematics
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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Ответ:
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
Ответ:
The correct answer is x = 2/5
Step-by-step explanation:
It is given an expression,
1/4x = 5/8
To solve the expression
The given expression is 1/4x = 5/8
(Cross multiply both sides we get)
8 = 5 * 4x
8 = 20x
20x = 8
x = 8/20
x = 2/5
Therefore the value of x = 2/5
The correct answer is x = 2/5