Question

Formulate a system of equations for the situation below and solve. The annual returns on Sid Carrington's three investments amounted to $21,600: 2% on a savings account, 8% on mutual funds, and 12% on bonds. The amount of Sid's investment in bonds was twice 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

Answer 1

Sid Carrington invested $43,200 in the savings account, $129,600 in mutual funds, and $86,400 in bonds.

Step-by-step explanation:

Let's start by assigning variables to represent the amounts of money invested in each account:

x = amount invested in the savings account

y = amount invested in mutual funds

2x = amount invested in bonds

Using the given information, we can write the following equations:

0.02x + 0.08y + 0.12(2x) = 21600

0.02x + 0.08y + 0.24x = 21600

0.26x + 0.08y = 21600

Also, we know that the interest earned from bonds is equal to the dividends from mutual funds:

0.12(2x) = 0.08y

0.24x = 0.08y

0.24x - 0.08y = 0

We now have a system of two equations with two variables:

0.26x + 0.08y = 21600

0.24x - 0.08y = 0

We can solve this system of equations by elimination or substitution method. Let's use the elimination method:

Multiplying the first equation by 100 on both sides:

26x + 8y = 2160000

Multiplying the second equation by 25 on both sides:

6x - 2y = 0

Multiplying the second equation by 4 on both sides:

24x - 8y = 0

Adding the modified second equation to the first equation:

26x + 8y + 24x - 8y = 2160000 + 0

50x = 2160000

x = 43200

Substituting the value of x into the second equation:

6x - 2y = 0

6(43200) - 2y = 0

259200 - 2y = 0

2y = 259200

y = 129600

Now we can find the value of the investment in bonds (2x):

2x = 2(43200) = 86400

Therefore, the amounts of money invested by Sid Carrington are $43,200 in the savings account, $129,600 in mutual funds, and $86,400 in bonds.