Question

Maricopa's Success scholarship fund receives a gift of $ 200000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.8 % interest, and stocks pay 6.6 % interest. Maricopa Success invests $ 50000 more in bonds than in CDs. If the annual income from the investments is $ 10497.5 , how much was invested in each account?

Answer 1

Let x be the amount invested in CDs

Let y be the amount invested in bonds

Let z be the amount invested in stocks

The money is invested in stocks, bonds and CDs:

`x+y+z=200000`

CDs pay 3.25 % interest, bonds pay 4.8 % interest, and stocks pay 6.6 % interest, the annual income from the investments is $ 10497.5:

`0.0325x+0.048y+0.06z=10497.5`

Maricopa Success invests $ 50000 more in bonds than in CDs:

`y=x+50000`

____________

Solve the next system of equations:

`\begin{gathered} x+y+z=200000 \\ 0.0325x+0.048y+0.06z=10497.5 \\ y=x+50000 \end{gathered}`

1. Use the third equation to substitute the y in the frist equation by (x+50000):

`x+x+50000+z=200000`

2. Solve z in terms of x:

`\begin{gathered} 2x+50000+z=200000 \\ 2x+z=200000-50000 \\ 2x+z=150000 \\ z=150000-2x \end{gathered}`

3. Write the second eqation in terms of x (use third equation and the equation you get inprevious step):

`0.0325x+0.048(x+50000)+0.066(150000-2x)=10497.5`

4. Solve x:

`\begin{gathered} 0.0325x+0.048x+2400+9900-0.132x=10497.5 \\ -0.0515x+12300=10497.5 \\ -0.0515x=10497.5-12300 \\ -0.0515x=-1802.5 \\ x=(-1802.5)/(-0.0515) \\ \\ x=35000 \end{gathered}`

5. Use the value of x to solve the other variables:

`\begin{gathered} y=x+50000 \\ y=35000+50000 \\ y=85000 \\ \\ z=150000-2x \\ z=150000-2(35000) \\ z=150000-70000 \\ z=80000 \end{gathered}`

The solution for the system is:

x=35000

y=85000

z=80000

Then, Maricopa Success scholarship fund invested the money as follow:

Maricopa Success invested $80000 in stocks

Maricopa Success invested $85000 in bonds

Maricopa Success invested $35000 i CDs