assignment 9.2: systems of linear equations: three variables\nscore: 7/9 answered: 7/9\nquestion…

assignment 9.2: systems of linear equations: three variables\nscore: 7/9 answered: 7/9\nquestion 8\nmaricopas success scholarship fund receives a gift of $ 175000. the money is invested in stocks, bonds, and cds. cds pay 3.75 % interest, bonds pay 4.8 % interest, and stocks pay 6.2 % interest. maricopa success invests $ 40000 more in bonds than in cds. if the annual income from the investments is $ 8365, how much was invested in each account?\nmaricopa success invested $ \nmaricopa success invested $ \nmaricopa success invested $ \nquestion help: video post to forum

assignment 9.2: systems of linear equations: three variables\nscore: 7/9 answered: 7/9\nquestion 8\nmaricopas success scholarship fund receives a gift of $ 175000. the money is invested in stocks, bonds, and cds. cds pay 3.75 % interest, bonds pay 4.8 % interest, and stocks pay 6.2 % interest. maricopa success invests $ 40000 more in bonds than in cds. if the annual income from the investments is $ 8365, how much was invested in each account?\nmaricopa success invested $ \nmaricopa success invested $ \nmaricopa success invested $ \nquestion help: video post to forum

Answer

Explanation:

Step1: Define variables

Let $x$ be the amount invested in CDs, $y$ be the amount invested in bonds, and $z$ be the amount invested in stocks. We know that:

  1. The total amount of money invested is $175000$, so $x + y+z=175000$.
  2. The amount invested in bonds is $40000$ more than in CDs, so $y=x + 40000$.
  3. The annual - income from the investments is $8365$. The interest from CDs is $0.0375x$, from bonds is $0.048y$, and from stocks is $0.062z$. So $0.0375x+0.048y + 0.062z=8365$.

Step2: Substitute $y$ in the first two equations

Substitute $y=x + 40000$ into $x + y+z=175000$: $x+(x + 40000)+z=175000$ $2x+z=175000 - 40000$ $2x+z=135000$, so $z=135000 - 2x$. Substitute $y=x + 40000$ into $0.0375x+0.048y + 0.062z=8365$: $0.0375x+0.048(x + 40000)+0.062z=8365$ $0.0375x+0.048x+1920+0.062z=8365$ $0.0855x+0.062z=8365 - 1920$ $0.0855x+0.062z=6445$.

Step3: Substitute $z$ into the second - substituted equation

Substitute $z = 135000-2x$ into $0.0855x+0.062z=6445$: $0.0855x+0.062(135000 - 2x)=6445$ $0.0855x+8370-0.124x=6445$ $0.0855x-0.124x=6445 - 8370$ $-0.0385x=-1925$ $x=\frac{-1925}{-0.0385}=50000$.

Step4: Find $y$ and $z$

Since $y=x + 40000$, then $y=50000 + 40000=90000$. Since $z=135000 - 2x$, then $z=135000-2\times50000=135000 - 100000 = 35000$.

Answer:

Maricopa Success invested $$35000$ in stocks. Maricopa Success invested $$90000$ in bonds. Maricopa Success invested $$50000$ in CDs.