Answer:
Step-by-step explanation:
Total amount borrowed by the museum is $2000000
Let x represent the amount borrowed at 7%
Let y represent the amount borrowed at 8.5%
Let z represent the amount borrowed at 9.5%.
The formula for simple interest is
l = PRT/100
Where
I = interest
P = principal
R = rate
T = time
For a Pincipal of $x borrowed at a rate of 7% and the time is 1 year,
the simple interest would be expressed as
I = (x × 7 × 1)/100 = 0.07x
Fora Principal of $y borrowed at a rate of 8.5% and a duration of 1 year, the simple interest would be expressed as
I = (x × 8.5 × 1)/100 = 0.085y
For a Principal of $z borrowed at rate of 9.5% and a duration of 1 year,
the simple interest would be expressed as
I = (x × 9.5 × 1)/100 = 0.095z
The total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. This means that
y = 4z
The total annual interest would be expressed as
169750 = 0.07x + 0.085×4z + 0.095z
169750 = 0.07x + 0.34z + 0.095z
169750 = 0.07x + 0.435z
The museum borrowed $2,000,000 at simple annual interest. It means that
x + y + z = 2000000
Since y = 4z , then
x + 4z + z = 2000000
x + 5z = 2000000
So the equations are
x + 5z = 2000000
0.07x + 0.435z = 169750
