Problema Solution
An investment of 63,000 was made. The investment was split into three parts and lasted 1 year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $4950. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investments.
Answer provided by our tutors
Investment = $ 63,000
First Part: interest I1 = x * 0.08 where 'x' is the first part of the investment
Second Part: interest I2 = y * 0.06 where 'y' is the second part of the investment
Third Part: interest rate I2 = z * 0.09 where 'z' is the third part of the investment
We need to find x, y and z.
Using the conditions of the problem we have
x + y + z = 63,000
I1 + I2 + I3 = 4950
I1 = 4 * I2
or we get a system of 3 equations that we need to solve
x + y + z = 63,000 (1)
x * 0.08 + y * 0.06 + z * 0.09 = 4950 (2)
x * 0.08 = 4* y * 0.06 (3)
If we multply (3) from both sides by 100 and devide by 8 we get
x = 3y
From (1) we get z = 63,000 - x - y
z = 63,000 - 3y - y
z = 63,000 - 4y
Using x = 3y and z = 63,000 - 4y in (2) we get
3y * 0.08 + y * 0.06 + (63,000 - 4y) * 0.09 = 4950 /*100
24 y + 6 y + 567,000 - 36 y = 495,000
6 y = 567,000 - 495,000
6 y = 72,000
y = $12,000
x = 3 * 12,000 = $36,000
z = 63,000 - 4 * 12,000 = $15,000
The first part of the investment is $36,000, the second part of the investment is $12,000 and the third part of the investment is $15,000.