Question 360631: Mr. and Mrs. Wise put $6000 into three different investments paying 9.5%, 8.5% and 6.25%, respectively. The total simple annual cost at the end of 2 years was $970. The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%. How much was invested at each rate?
I'm having trouble setting up the third equation (the one from "The total simple annual cost at the end of 2 years was $970.)
I got:
x+y+z=6000
and
x+y-z=0
for the third one I got
19x+17y+12.5z=970
(I multiplied 9.5, 8.5, and 6.25 by 2)
but when I solved I got a negative number for x
what am I doing wrong?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Mr. and Mrs. Wise put $6000 into three different investments paying 9.5%, 8.5% and 6.25%, respectively.
The total simple annual cost at the end of 2 years was $970.
The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%. How much was invested at each rate?
I'm having trouble setting up the third equation (the one from "The total simple annual cost at the end of 2 years was $970.)
-------------
I got:
x+y+z=6000
and
x+y-z=0
for the third one I got
19x+17y+12.5z=970
(I multiplied 9.5, 8.5, and 6.25 by 2)
but when I solved I got a negative number for x
what am I doing wrong?
-------------------
x = amount at 9.5%
y = amount at 8.5%
z = amount at 6.25%
x + y + z = 6000
0.19x + 0.17y + 0.125z = 970
----------
The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%.
(x+y)/2 = z
------------
x + y + z = 6000
x + y -2z = 0 (This one is different)
38x+34y+25z = 194000
----------
Sub for z
--------
x + y + (x+y)/2 = 6000
3x + 3y = 12000
38x+34y+25(x+y)/2 = 194000
101x+93y = 388000
93x +93y = 372000
------------------ Subtract
8x = 16000
x = 2000
----------
y = 2000
z = 2000
|
|
|
