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Question 169402: Lin Hisa plans to invest $1,400 in two stocks: Consolidated Industries (CI) and Amalgamated Manufacturing (AM). Suppose that after 5 years Lin's CI stock does not change in value, but her AM stock triples, making her stocks worth $3,300. Write an equation that expresses this fact.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let x = amount of money invested in CI today
let y = amount of money invested in AM today.
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total invested in both equals $1400.
x + y = $1400
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5 years from now CI stock doesn't change in value.
5 years from now AM stock triples.
total value of both stocks in 5 years is $3300.
x + 3y = $3300
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you have two equations that you want to solve simultaneously.
x + y = 1400
x + 3y = 3300
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if you subtract the second equation from the firsts equation, the unknown variable of x will disappear.
you get:
(x - x) + (3y - y) = (3300 - 1400)
this becomes:
2y = 1900
y = 950
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substituting 950 for y in the first equation gets:
x + 950 = 1400
subtract 950 from both sides of the equation to get:
x = 1400 - 950
which becomes:
x = 450.
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you now have a value for x and y that should be able to satisfy both equations.
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first equation has already been satisfied since that is the equation where we solved for x.
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second equation is:
x + 3y = 3300
substituting 450 for x and 950 for y, we get:
450 + (3*950) = 3300
simplifying:
450 + 2850 = 3300
3300 = 3300
equation is satisfied.
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answer is:
x = amount invested in CI stock = $450
y = amount invested in AM stock = $950
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