SOLUTION: 3. Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested
Question 84209: 3. Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates? Answer by sofiyacherni(99) (Show Source):
You can put this solution on YOUR website! 3. Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?
Here is how you should approach this problem
Say she invested x dollars at 12%, to represent % as a number divide % by 100, so 12% is .12. Say she invested y dollars at 10%, so .10. From this she earned 130 dollars. So you have your first equation
.12x+.10y=130
Next if you interchange amounts invested and add 4 dollars to earnings you have sencond equation
.10x+.12y=134
so use substitution to solve a system of equations
(1) .12x+.10y=130
(2) .10x+.12y=134
so, from (2) .1x+.12y=134
(3) now sub this in (1) in place of x, you get now plug this value into (3), you get
So JANE invested $500 at 12% and $700 at 10% and
RANDY invested $700 at 12% and $500 at 10%
Good luck
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