SOLUTION: If I invest $25,000 in two different stocks. One earns 6.5% and the other earns 7.00%. If the total interest earnings for one year is 1683.75, how much is invested in each stock

Question 54880: If I invest $25,000 in two different stocks. One earns 6.5% and the other earns 7.00%. If the total interest earnings for one year is 1683.75, how much is invested in each stock?
Stock X = ? = 6.5% interest
Stock Y = ? = 7.0% interest
Total = $25,000 = 1,683.75 Total interest
Please show me how to solve this problem.
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If I invest $25,000 in two different stocks. One earns 6.5% and the other earns 7.00%. If the total interest earnings for one year is 1683.75, how much is invested in each stock?
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Let amount invested at 6.5% be "x".
Interest on this money is 0.065x dollars.
--------
Amount invested at 7% is "25000-x"
INterest on this money is 0.07(25000-x)=1750-0.07x dollars
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EQUATION:
interest + interest = 1683.75
0.065x + 1750-0.07x = 1683.75
-0.005x=-66.25
x=$13,250 (amount invested at 6.5%)
25000-x=$38,250 (amount invested at 7%)
Cheers,
Stan H.
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
Ax+By=C [Use the standand formula of a line]
A=the rate, percent or cost of item A
x=the amount or number of item A
B=the rate, percent or cost of item B
y=the rate, percent or cost of item B
C=(the total amount)(average rate)
x+y=C so y=(Total amount of C-x] or y=C-x [Substitution for the y variable]
.
(0.065)(x)+(0.07)(25,000-x)= 1683.75 [Plug-in the values]
0.065x+1750-0.07-x= 1683.75 [Simplify]
0.065x-0.07-x= 1683.75-1750 [Solve for x]
-.005x=-66.26
x=$13,250
.
(6.5%)($13,250)=(0.065)(13,250)=$861.25 invested at 6.5%
(7.0%)($25,000-x)=0.07(25,000-13,250)=1750-927.50=$822.50 invested at 7.0%
So, $861.25+$822.50=$1683.75

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