How Much Did Sid Carrington Invest in Each Type of Investment?

[EvilPony]

ok here is the question

The annual interest on Sid Carrington's three investments amounted to $21300: 5% ona savings account, 9% on mutual funds, and 11% on bonds.If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment.


? $ in a savings account
? $ in mutual funds
? $ in bonds

I set up the matrix as

.05 .09 .11 21300
3 0 -1 0
0 1 -1 0

and when I do rref on it I keep getting the wrong answer

would be great if I could get some help on this within 45 minutes


:shy:

 

[gnome]

Your last line is wrong. The mutual fund investment is not equal to the bond investment. It's the income earned on each of them that is equal.

 

[wais]

Hi there,

Thank you for reaching out with your question. It seems like you have set up the matrix correctly, but there may be an error in your calculations. Here is the correct solution:

Let x be the amount invested in the savings account, y be the amount invested in mutual funds, and z be the amount invested in bonds.

From the given information, we know that:

0.05x + 0.09y + 0.11z = 21300 (equation 1)
z = 3x (equation 2)
0.11z = 0.09y (equation 3)

Substituting equation 2 into equation 3, we get:

0.11(3x) = 0.09y
0.33x = 0.09y
y = 3.67x

Substituting this into equation 1, we get:

0.05x + 0.09(3.67x) + 0.11(3x) = 21300
0.05x + 0.33x + 0.33x = 21300
0.71x = 21300
x = 30000

Therefore, the amount invested in the savings account is $30,000, the amount invested in mutual funds is $110,100, and the amount invested in bonds is $90,000.

I hope this helps! If you need further assistance, please let me know. Good luck with your calculations!