SOLUTION: Carlos invested part of $2000 in a 10% certificate account and the rest in a 6% passbook account. The total annual interest from both accounts is $180. How much did he invest at 6%

Question 1096643: Carlos invested part of $2000 in a 10% certificate account and the rest in a 6% passbook account. The total annual interest from both accounts is $180. How much did he invest at 6%?
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
10% certificate:
Principal = p
Rate = 0.10
Interest = 0.10p

6% passbook:
Principal = 2000 - p
Rate = 0.06
Interest = 0.06(2000 - p) = 120 - 0.06p

Total interest:

0.10p + (120 - 0.06p) = 180

Simplify:

0.04p = 60

Solve for p:

p = 1500

From earlier:

6% passbook:
Principal = 2000 - p = 2000 - 1500 = 500

Carlos invested $500 at 6%.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a method for solving mixture problems like this which, if you understand it, can get you to the answers much faster and with far less effort than the traditional algebraic method shown by the other tutor.

(1) $180 interest on $2000 means a 9% interest rate. (180/2000 = .09 = 9%)
(2) 9% is 3/4 of the way from 6% to 10%. (the overall interest rate is 3/4 of the way from the lower to the higher interest rate)
(3) Therefore, 3/4 of the money was invested at the higher rate.

ANSWER: the amount invested at the lower rate was 1/4 of the total of $2000, which is $500.
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