SOLUTION: An investment of $37000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, t
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Question 1199034: An investment of $37000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $3030 The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.
There are several ways you could set this up directly using three variables for the amounts in each investment. But that would require three equations, and some method for solving a system of three equations.
I always prefer to take a little time to process the given information so that I can set up the problem using a single variable. Because of the way the information is given in this problem, that takes some effort; but I feel it is worth it.
I hope you get responses from other tutors showing different ways of setting up and solving the problem.
Given the information that the interest from the investment at 8% is 6 times the interest from the investment at 6%, do some mental arithmetic (or use formal algebra) to determine that the amount invested at 8% is 4.5 times the amount invested at 6%. (8% of 4.5x is 6 times 6% of x...)
Then
let 2x = amount invested at 6%
then 9x = amount invested at 8%
then 37000-11x = amount invested at 9%
Note I chose 2x and 9x, instead of x and 4.5x, to represent the amounts invested at 6% and 8%. That's just a personal preference for avoiding fractions or decimals in my equations....
The total interest was $3030:
The amounts invested at the three rates were
ANSWERS:
2x = $4000 at 6%
9x = $18000 at 8%
$37000-11x = $15000 at 9%
