Problema Solution
An investment of $88,000 was made by a business club. The investment was split into three parts and lasted for one year. The first party of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $6660. The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of the investment.
Answer provided by our tutors
Investment = $ 88,000
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 = 88,000
I1 + I2 + I3 = 6660
I1 = 3 * I2
or we get a system of 3 equations that we need to solve
x + y + z = 88,000 (1)
x * 0.08 + y * 0.06 + z * 0.09 = 6660 (2)
x * 0.08 = 3* y * 0.06 (3)
If we multply (3) from both sides by 100 and devide by 2 we get
4 x = 9 y
x = (9/4) y
From (1) we get z = 88,000 - x - y
z = 88,000 - (9/4) y - y
z = 88,000 - (13/4) y
Using x = (9/4) y and z = 88,000 - (13/4) y in (2) we get
(9/4) y * 0.08 + y * 0.06 + (88,000 - (13/4) y) * 0.09 = 6660 /*100
18 y + 6 y + 792,000 - (117/4) y = 666,000
(45/4) y = 792,000 - 666,000
y = 11,200
y = $11,200
x = (9/4) * 11,200 = $25,200
z = 88,000 - (26,400 + 59,400) = $51,600
The first part of the investment is $25,200 the second part of the investment is $11,200 and the third part of the investment is $51,600.