SOLUTION: Nithya has money invested in 3 accounts: Account A earns 3% interest, Account B earns 4%, and Account C earns 5%. The money invested in Account B is 4,000 less than the money in ac

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Nithya has money invested in 3 accounts: Account A earns 3% interest, Account B earns 4%, and Account C earns 5%. The money invested in Account B is 4,000 less than the money in ac      Log On


   

Question 1174543: Nithya has money invested in 3 accounts: Account A earns 3% interest, Account B earns 4%, and Account C earns 5%. The money invested in Account B is 4,000 less than the money in account A. The money invested in Account C is twice the amount in Account A. A total of $1,540 was earned in total interest for the year. What was the total amount of money invested between the 3 accounts at the start of the year?
I tried this:
x=account A, y= account B, z= account C
0.03x=0.04y+4,000
0.05z=0.06x
0.03x+0.04y+0.05z=1540
But some numbers were negative. What's wrong with my equations?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

Account A   x  dollars

Account B   (x-4000)  dollars.

Account C   2x  dollars.



The total interest equation

    0.03x + 0.04*(x-4000) + 0.05*(2x) = 1540   dollars.



Simplify and solve.


I leave it to you.


The lesson to learn from my post is THIS:

        You don't need use 3 unknown.
        Solve the problem using ONE UNKNOWN, ONLY

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Nithya has money invested in 3 accounts: Account A earns 3% interest, Account B earns 4%, and Account C earns 5%. The money invested in Account B is 4,000 less than the money in account A. The money invested in Account C is twice the amount in Account A. A total of $1,540 was earned in total interest for the year. What was the total amount of money invested between the 3 accounts at the start of the year?
I tried this:
x=account A, y= account B, z= account C
0.03x=0.04y+4,000
0.05z=0.06x
0.03x+0.04y+0.05z=1540
But some numbers were negative. What's wrong with my equations? 
I agree with Tutor @IKLEYN that 1 variable is sufficient to solve problems such as this one.



Let the amount invested in Company A be A

Then amounts invested in Company B and Company C were: A - 4,000, and 2A, respectively

We then get: .03A + .04(A - 4,000) + .05(2A) = 1,540

.03A + .04A - 160 + .1A = 1,540

.17A = 1,700

Amount invested in Company A, or 

You should now be able to find the amounts that were invested in Companies B & C!