Formulate but do not solve the problem The annual returns on

Formulate but do not solve the problem. The annual returns on Sid Carrington\'s three investments amounted to $19, 040: 4% on a savings account, 7% on mutual funds, and 13% 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 he placed in each type of investment. (Let x, y, and z denote the amount, in dollars. In savings, mutual funds, and bonds, respectively.)

Solution

Let the deposit in Savings is x, in Mutual funds it is y and in Bonds it is z.

we have 4% on savings account , 7% on mutual funds and 13% on bonds.

total annual return is $19040.

so we can say that

0.04x + 0.07y + 0.13z = $19040

The amount of sid\'s investment in bonds was teice the amount of investment in savings account

so we can say that ,

z = 2z hence 2x - z = 0

and the interest earned from his investment in bonds was equal to the divident from mutual funds hence we can say that,

0.07y = 0.13z

7y - 13z = 0

so we have total 3 equations

0.04x + 0.07y + 0.13z = $19040 --------------1)

2x - z = 0 -----------------2)

7y - 13z = 0 ----------3)

we can write equation 1) as

4x + 7y + 13z = 1904000 -----4)

now put 2x = z and 7y = 13z in equation 4) we have,

2z + 13z + 13z = 1904000

28z = $1904000 so z = $68000

from 2) we have 2x - z = 0 so 2x = z

we have z = $68000

so 2x = $68000 so x = $34000

from 3) we have 7y - 13z = 0 so 7y = 13z

we have z = $68000

so 7y = 13*$68000 so y = $126285.7143

we have,

deposit in Savings is x = $34000

deposit in Mutual funds is y = $126285.7143

deposit in Bonds is z = $68000