SOLUTION: An investor decides to invest some cash in the account paying 14% annual interest and to put the rest in a stock fund the ends up earning 10% over the course of a year. The investo

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Question 928376: An investor decides to invest some cash in the account paying 14% annual interest and to put the rest in a stock fund the ends up earning 10% over the course of a year. The investor puts $1500 more in the first account then in the stock fund, and at the end of the year finds the total interest from the 2 investments was $1020. how much money was invested at each of the two rates?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We don't know the total invested.
We know the difference in the two accounts.
We know that the interest for the two accounts is $1020
0.14*x+0.1*y=1020
We know that the account at 14% has $1500 more.
x=1500+y
We substitute for x
0.14*(1500+y)+0.1*y=1020
We multiply out
210+0.14y+0.1*y=1020
We combine like terms.
0.24*y=810
Isolate y
y=$3375 at 10%
x=1500+y
Calculate x
x=$4875 at 14%
Now,we know the total invested is: 8250
Total invested $4875+$3375=$8250
We check
0.14*4875+0.1*3375=1020
682.5+337.5=1020
1020=1020
Since this statement is TRUE and neither x nor y is negative all is well.
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