SOLUTION: Solve the problem. Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The inco

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Solve the problem. Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The inco      Log On


   

Question 423919: Solve the problem.
Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The income from the 5% amd 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate.


Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5% ---------------- x
6% -----------------y
8% ----------------25000-(x+y)
0.05x+0.06y+0.08(25000-(x+y))=1600
0.05x+0.06y+2000-0.08x-0.08y=1600
-0.03x-0.02y=-400...............1
0.05x+0.06y=0.08(25000-(x+y))
0.05x+0.06y=2000-0.08x-0.08y
0.13x+0.14y=2000.................2
-0.03x-0.02y=-400.............1
0.13x+0.14y=2000 .............2

multiply (1)by 7
Multiply (2) by 1
-0.21x-0.14y=-2800
0.13x+0.14y=2000

Add the two equations -0.08x=-800
/-0.08
x=10000
plug value of x in (1)

-0.03x-0.02y=-400
-300-0.02y=-400
-0.02y=-400+ 300
-0.02y=-100
y=5000
x+y = 15000
25000 -15000 = 10,000 invested at 8 %