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Question 1186847: Maria has money in two investment funds. last year, the first fund paid a dividend of 8% and the second a dividend of 2%, and she received a total of $780. This year, the first fund paid a 10% dividend and the second only 1% and she received $810. How much does she have invested in each fund?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x equals the first investment.
y = the second investment.
your two equations that need to be solved simultaneously are:
.08 * x + .02 * y = 780
.10 * x + .01 * y = 810
multiply both sides of the second equation by 2 and leave the first equation as is to get:
.08 * x + .02 * y = 780
.20 * x + .02 * y = 1620
subtract the first equation from the second to get:
.12 * x = 840
solve for x to get:
x = 840 / .12 = 7000
in the first original equation, replace x with 7000 to get:
.08 * x + .02 * y = 780 becomes:
.08 * 7000 + .02 * y = 780
simplify to get:
560 + .02 * y = 780
subtract 560 from both sides of the equation to get:
.02 * y = 220
solve for y to get:
y = 220 / .02 = 11000
you have:
x = 7000 and y = 11000.
that's your answer.
confirm by replacing x with 7000 and y with 1100 in the original two equations.
you get:
.08 * x + .02 * y = 780 becomes .08 * 7000 + 02 * 11000 = 780 which becomes 560 + 220 = 780 which becomes 780 = 780, confirming the value of x and y in the first equation is good.
.10 * x + .01 * y = 810 becomes .10 * 7000 + .01 * 11000 = 810 which becomes 700 + 110 = 810 which becomes 810 = 810, confirming the value of x and y in the second equation is good.
your solution of x = 7000 and y = 11000 is confirmed to be good.
that's how much she invested in each fund.
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