Linear Systems

Question

Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. CDs pay 4.25 % interest, bonds pay 3.3 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 20000 more in bonds than in CDs. If the annual income from the investments is $ 7260 , how much was invested in each account?

Maricopa Success invested $__________in stocks.
Maricopa Success invested $ __________in bonds.
Maricopa Success invested $ ___________in CDs.

Answer 1

The only thing hard about this problem is the arithmetic, which will trip you up!  Be careful!  I had to go through it several times before I got it right.

 

Let S = the amt in stocks, B in bonds and C is CDs

 

S + B + C = 145000

.113S + .033B + .0425C = 7260

B = C + 20000

 

substitute for B and get rid of the decimals by multiplication

S + C + 20000 + C = 145000

1130S + 330(C + 20000) = 425C = 72600000

 

Expand and collect

S + 2C = 125000

1130 + 755C = 66000000

 

The easiest way from this point is with a determinant, but since that is probably not an option known to you,

substitute for S

 

1130(125000 - 2C) + 755C = 66000000

141250000 - 2260C + 755C = 66000000

75250000 = 1505C

C = 50000

B = 70000

S = 145000 - 120000 = 45000

 

You should take these values and make sure that the interest equation checks out!

 

 

 

Answer 2

Create a three variable system of equations

Let: x=amt invested in stocks, y=amt in bonds, and y= amt in cds

System of equations:

x+y+z=145000

.113x+.033Y+.0425z=7260

y-z=20000 Note: y=z+20000 per the problem

You may solve this system using Gauss-Jordon elimination and place the system in reduced row echelon form or use your graphing calculator to solve the system.

Answer:Stocks⇒$25,000, Bonds⇒$70,000, and CDs⇒$50,000