a person invested $7000 for 1 year, part at 5%, part at 10%, and the remainder at 15%.

Question

the full question:

A person invested $7000 for 1 year, part at 5%, part at 10%, and the remainder at 15%. The total annual income from these investments was $815. The amount of money invested at 15% was $200 more than the amount invested at 5% and 10% combined. Find the amount invested at each rate.

Answer 1

x=amt invested at .05

y=amt invested at .1

z=amt invested at .15

 

equation 1:  x+y+z=7000

equation 2:  .05x+.1y+.15z=815

 

Note: z = 200+x+y

Plug z into equation 1

x+y+(200+x+y)=7000

2x+2y=6800

equation 3:  x+y=3400

 

Plug z into equation 2

.05x+.1y+.15(200+x+y)=815

.2x+.25y+30=815

.2x+.25y=785

 

multiply equation 1 by -.2 and add it to equation 2:

-.2x-.2y=-680

+

.2x+.25y+785

.05y=105

y=2100

 

Plug y into equation 3 and solve for x:

x+2100=3400

x=1300

 

We know that z = 200+x+y

Plug x and y into the z equation to solve for z

z=200+1300+2100

z=3600

 

x=1300

y=2100

z=3600