SOLUTION: man invests $2500 in two accounts. one account earns 2% and the other account earns 9%.the total profit is $113.How much is invested in the two accounts

Question 1099892: man invests $2500 in two accounts. one account earns 2% and the other account earns 9%.the total profit is $113.How much is invested in the two accounts

Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Total amount of money invested: $2500
x+y=2500,
Total yearly interest for the two accounts is: $113
0.02*x+0.09*y=113
x=2500-y
Substitute for x
0.02*(2500-y)+0.09*y=113
Multiply out
50-0.02*y+0.09*y=113
Combine like terms.
0.07*y=63
Isolate y
y=$900.00 at 9% earns $81 interest
x=2500-y
Calculate x
x=$1600.00 at 2% earns $32 interest
Check
0.02*1600+0.09*900=113
32+81=113
113=113
codeint1
Tutor greenestamps,
I always enjoy seeing your alternate methods of solution.
Thanks.

Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!

Here are two variations of an alternative method for solving this kind of problem. If you understand either of them, you will get to the answer much faster and with far less work than the traditional algebraic method shown by the other tutor.

First variation...

(1) $2500 all invested at 2% would yield $50 interest; $2500 all at 9% would yield $225 interest.
(2) The actual amount of interest, $113, is 9/25 of the distance from $50 to $225. (; ;
(3) Therefore, 9/25 of the $2500, or $900, is invested at 9%; the remaining 16/25, or $1600, is invested at 2%.

And here is a structured method for doing the same calculations....

(1) Start with a "tic-tac-toe" game board, with 50 and 225 (the amounts of interest if all the $2500 were invested at the individual rates) in the top and bottom left columns, and the actual amount of interest in the middle spot:

(2) Working diagonally, put the positive differences between the numbers in the first column and the number in the second column into the appropriate squares in the third column:

(3) The ratio of the two numbers in the third column, 112:63 or 16:9, is the ratio in which the $2500 must be divided: 16/25 or $1600 at the lower 2% rate, and 9/25 or $900 at the higher 9% rate.

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