An investment of $29,000 was made divided into 3 parts for 1 year. Part 1) earned 8%, 2) 6%, 3) 9%. =$2250. Part 1 earned 4x more than part 2.

Question

An investment of $29,000 was made by a business group. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6% interest, and the third 9% interest. The total interest earned from the investments was $2250. The interest from the first investment was four times the interest from the second. Find the amounts of the three parts of the investments.

Answer 1

Hi D.

 

Let's call some variables.

 

A = amount invested into 8% account

B = amount invested into 6% account

C = amount invested into 9% account

 

The first sentence says that you made an investment of $29,000. That translates to:

 

A + B + C = 29000

 

The third sentence states that the total interest earned from every investment was $2,250. Since you know the rate of return for each account, you can write your second equation:

 

0.08*A + 0.06*B + 0.09*C = 2250

 

The fourth sentence then states that the interest from the first investment (0.08*A) was 4x the interest from the second investment (0.06*B). This translates to:

 

0.08*A = 4*(0.06*B)

0.08*A = 0.24*B

 

or

 

0.08*A - 0.24*B = 0

 

So now you have a system of equations:

 

A + B + C = 29000

0.08*A + 0.06*B + 0.09*C = 2250

0.08*A - 0.24*B = 0

 

You can write this as a matrix:

 

1        1       1        29000

0.08   0.06   0.09   2250

0.08   -0.24  0       0

 

and use any kind of matrix resolver to solve it. I like the ease of Wolfram's. Here's the syntax:

 

rref([1,1,1,29000],[0.08,0.06,0.09,2250],[0.08,-0.24,0,0])

 

rref = reduced row echelon form.

 

It'll spit out this:

 

1 0 0 18000

0 1 0 6000

0 0 1 5000

 

That tells you

 

A = $18,000 (amount invested in the 8% account)

B = $6,000 (amount invested in the 6% account)

C = $5,000 (amount invested in the 9% account)

 

Hope this helps.