Answer:
First Part = $54,000
Second Part = $12,000
Third Part = $15,000
Explanation:
Let the first part be "x"
2nd part be "y", and
3rd part be "z"
Total money is 81,000, thus we can write:
x + y + z = 81000
Now, total interest is 6390 from each part with respective percentages, so we can write:
0.08x + 0.06y + 0.09z = 6390
Also,
Interest from 1st is 6 times interest from 2nd, so we can write:
0.08x = 6* (0.06y)
0.08x = 0.36y
x = 4.5y
Now replacing this in 2nd equation, we get:
0.08x + 0.06y + 0.09z = 6390
0.08(4.5y) + 0.06y + 0.09z = 6390
0.36y + 0.06y + 0.09z = 6390
0.42y + 0.09z = 6390
replacing x = 4.5y into 1st equation, we get:
x + y + z = 81000
4.5y + y + z = 81000
5.5y + z = 81000
Multiplying this by -0.09, we have:
-0.09 * (5.5y + z = 81000)
= -0.495y - 0.09z = -7290
Adding this and previous equation:
0.42y + 0.09z = 6390
-0.495y - 0.09z = -7290
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-0.075y = -900
y = 12000
x = 4.5y
So,
x = 4.5(12,000) = 54000
x = 54000
z would be:
12000 + 54000 + z = 81000
z = 15000
