Question

Please help me asap

Answer 1

A. x+y+z=35,000

4x+6y+12x-194,000

2y-z=0

Explanation:

The system of equations is:

x + y + z = 35,000 (total investment is $35,000) 4x + 6y + 12z = 19,400 (the investor wants an annual return of $1940 on the three investments) y = 2z (the client wants to invest twice as much in A bonds as in B bonds)

The answer is A.

The first equation represents the total amount of money invested in the three types of bonds. The second equation represents the total annual return on the investments, which is equal to the sum of the individual returns on each type of bond. The third equation represents the client's preference for investing in A bonds over B bonds.

The system of equations can be used to solve for the values of x, y, and z, which represent the amounts invested in AAA, A, and B bonds, respectively.

Answer 2

`\textsf{A.} \quad \begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}`

Explanation:

A system of equations is a set of two or more equations with the same variables. It allows us to model and solve problems that involve multiple equations and unknowns.

An investment firm recommends that a client invest in bonds rated AAA, A, and B. The definition of the variables are:

• Let x be the number of AAA bonds.
• Let y be the number of A bonds.
• Let z be the number of B bonds.

The average yield on each of the three bonds is:

• AAA bonds = 4%
• A bonds = 6%
• B bonds = 12%

We have been told that the total investment is $35,000. Therefore, the equation that represents this is the sum of the three investments equal to 35,000:

`x+y+z=35000`

To find the annual return on each investment, multiply the number of bonds by the average yield (in decimal form). Given the investor wants a total annual return of $1940 on the three investments, the equation that represents this is the sum of the product of the investment amount for each bond type and its corresponding yield, equal to $1940.

`0.04x+0.06y+0.12z=1940`

Multiply all terms by 100:

`4x+6y+12z=194000`

Finally, given the client wants to invest twice as much in A bonds as in B bonds, the equation is:

`y=2z`

Subtract y from both sides of the equation:

`2z-y=0`

Therefore, the system of equations the models the given scenario is:

`\begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}`