Question 429409: You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330. This year, the first fund paid a 12% dividend and the second only 2% and you received a total of $1500. How much money did you invest in each fund?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Fund I x
Fund II ------------ y
0.08x+0.05y=1330 .............1
0.12x+0.02y=1500 .............2
multiply (1)by 5
Multiply (2) by 3
0.4 x + -0.02 y = 6650
0.36 x + 0.05 y = 4500
Add the two equations
0.76x=11150
/0.76
x=14671 Fund I
plug value of x in (1)
0.08x+0.05y=1330
1173.68 +0.05y= 1330
0.05y=1330-1173.68
0.05y= 156.32
y=3126 Fund II
neglect decimals
Answer by ikleyn(53541)  (Show Source):
You can put this solution on YOUR website! .
You invested money in two funds.
Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.
This year, the first fund paid a 12% dividend and the second only 2% and you received a total of $1500.
How much money did you invest in each fund?
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The solution in the post by @mananth is incorrect.
I came to bring a correct solution.
Write equations for the annual dividends for the 1st year and for the 2nd year,
as you read the problem
0.08x + 0.05y = 1330 (1)
0.12x + 0.02y = 1500 (2)
Multiply equation (1) by 2 (both sides). Multiply equation (2) by 5 (both sides). You will get
0.16x + 0.10y = 2660 (1')
0.60x + 0.10y = 7500 (2')
From equation (2'), subtract equation (1'). You will get
0.44x = 7500 - 2660
0.44x = 4840
x = 4840/0.44 = 11000.
Then from equation (1)
y =  = 9000.
CHECK. Equation (1), left side 0.08*11000 + 0.05*9000 = 1330 dollars. ! correct !
Equation (2), left side 0.12*11000 + 0.02*9000 = 1500 dollars. ! correct !
ANSWER. $11000 were invested in the first fund and $9000 were invested in the second fund.
Solved correctly by the Elimination method.
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