Eric C. answered • 02/17/16

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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.