Question

Chelsea invests a total of $17,500 in three products. She invests one part in a mutual fund which has an annual return of 11%. She invests the second part in government bonds at 7% per year. The third part she puts in CDs at 5% per year. She invests twice as much in the mutual fund as in the CDs. In the first year Chelsea's investments bring a total return of $1495. How much did she invest in each product? Show work.

Answer 1

x amount invested in mutualfund......gives 11%......= 0.11x

y amount invested in goverment bond .......gives 7%.......0.07

z amount invested in in CD .......gives 5%......0.05z

.
total interest is = 1495

0.11x + 0.07y + 0.05z = 1495

11x + 7x + 5x = 149500.......(1)

.
.
total money x + y + z = 17500.......(2)

.
.
she invest twice as much in the mutual fund as in the CD

x = 2z

x - 2z = 0...........(3)

for above three equations augmented matrix is

11	7	5	149500
1	1	1	17500
1	0	-2	0

convert into  Reduced Row Eschelon Form...

Divide row1 by 11

1	7/11	5/11	149500/11
1	1	1	17500
1	0	-2	0

Add (-1 * row1) to row2

1	7/11	5/11	149500/11
0	4/11	6/11	43000/11
1	0	-2	0

Add (-1 * row1) to row3

1	7/11	5/11	149500/11
0	4/11	6/11	43000/11
0	-7/11	-27/11	-149500/11

Divide row2 by 4/11

1	7/11	5/11	149500/11
0	1	3/2	10750
0	-7/11	-27/11	-149500/11

Add (7/11 * row2) to row3

1	7/11	5/11	149500/11
0	1	3/2	10750
0	0	-3/2	-6750

Divide row3 by -3/2

1	7/11	5/11	149500/11
0	1	3/2	10750
0	0	1	4500

Add (-3/2 * row3) to row2

1	7/11	5/11	149500/11
0	1	0	4000
0	0	1	4500

Add (-5/11 * row3) to row1

1	7/11	0	127000/11
0	1	0	4000
0	0	1	4500

Add (-7/11 * row2) to row1

1	0	0	9000
0	1	0	4000
0	0	1	4500

x = 9000 amount invested in mutual fund

y = 4000  amount invested in goverment bond

z = 4500  amount invested in in CD