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Sagot :
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:
[tex]x+y+z=200000[/tex]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:
[tex]0.0325x+0.048y+0.06z=10497.5[/tex]Maricopa Success invests $ 50000 more in bonds than in CDs:
[tex]y=x+50000[/tex]____________
Solve the next system of equations:
[tex]\begin{gathered} x+y+z=200000 \\ 0.0325x+0.048y+0.06z=10497.5 \\ y=x+50000 \end{gathered}[/tex]1. Use the third equation to substitute the y in the frist equation by (x+50000):
[tex]x+x+50000+z=200000[/tex]2. Solve z in terms of x:
[tex]\begin{gathered} 2x+50000+z=200000 \\ 2x+z=200000-50000 \\ 2x+z=150000 \\ z=150000-2x \end{gathered}[/tex]3. Write the second eqation in terms of x (use third equation and the equation you get inprevious step):
[tex]0.0325x+0.048(x+50000)+0.066(150000-2x)=10497.5[/tex]4. Solve x:
[tex]\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=\frac{-1802.5}{-0.0515} \\ \\ x=35000 \end{gathered}[/tex]5. Use the value of x to solve the other variables:
[tex]\begin{gathered} y=x+50000 \\ y=35000+50000 \\ y=85000 \\ \\ z=150000-2x \\ z=150000-2(35000) \\ z=150000-70000 \\ z=80000 \end{gathered}[/tex]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
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