SOLUTION: Karen and John both inherited equal amounts of money and decided to invest them in two different banks One investment earns 5% and the other 7% John invested part of his money

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Question 32311: Karen and John both inherited equal amounts of money and decided to invest them in two different banks
One investment earns 5% and the other 7%
John invested part of his money at 5% and the rest 7% After a year his investment earned him $2700
Karen invested at 5% the amount John ivested at 7% She also invested 7% of the amount that John invested at 5% Her investment earned her $3300 after one year
How much did Karen invest at
5%
7%
How much did John invest at
5%
7%
Found 2 solutions by mukhopadhyay, checkley71:
Answer by mukhopadhyay(490) (Show Source):
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Assume John invested x dollars at 5% rate and y dollars at 7% rate
Thus, Karen invested y dollars at 5% rate and x dollars at 7% rate
2700 = .05x + .07y.... (1)
3300 = .07x + .05y.... (2)
Mult (1) with -5 and (2) with 7
-13500 = -.25x - .35y
23100 = .49x + .35y
......................
9600 = .24x (by summing above equations)
=> x = 9600/.24 = 40000
Using (1)
2700 = 2000 + .07y
=> y = 700/.07 = 10000
Answer: Karen invested $40,000 at 5% and $10,000 at 7%; John the other way.

Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
THE AVERAGE INVESTMENT FOR BOTH KAREN & JOHN WERE 6% THEREFORE THE AVERAGE PROFIT WAS 3000 OR (2700+3300)/2=3000 THEREFORE AN AVERAGE 6% INVESTMENT THAT EARNS 3000 MUST BE AN AMOUNT EQUAL TO 3000/.06 OR 50000
DETERMINING THE INVESTMENT VALES @ 5% & 7% WE GET
.05X+.07(50000-X)=2700 FOR JOHN OR .05X+3500-.07X=2700 OR -.02X=-800 OR X=40000
@ 5% AND THE REMAINDER OF 10000 @ 7%
KAREN INVESTED HER 40000 @ 7% AND THE REMAINDER OF 10000 @ 5% OR
.07(40000)+.05(10000)=3300 OR 2800+5000=3300