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Question 902343: please help me solve and explain this word problem:
An investment club invested part of $8000 at 10% annual interest and the rest at 12%. If the annual income from these investments is $900, how much was invested at each rate?
I understood to have "let" statements. So my "let" statements are: let x=10% annual interest and let Y=12% annual interest. I know to find two equations; how much is invested but I don't know the other one.
Thank you for reading and trying to answer my questions.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! please help me solve and explain this word problem:
An investment club invested part of $8000 at 10% annual interest and the rest at 12%. If the annual income from these investments is $900, how much was invested at each rate?
I understood to have "let" statements. So my "let" statements are: let x=10% annual interest and let Y=12% annual interest. I know to find two equations; how much is invested but I don't know the other one.
Thank you for reading and trying to answer my questions.
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Let
x = amount (in dollars) invested at 10%
y = amount (in dollars) invested at 12%
You can only pick one account or the other. Because you have $8000 total to invest, which is broken up, you will have this equation
That means that the sum of the two pieces must add back up to $8,000.
Solve for y:
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If you invest x dollars at 10% simple annual interest, then you earn  dollars in interest alone just from that investment.
Similarly, if you invest y dollars at 12% simple annual interest, then you earn  dollars.
Combined you earn  dollars annually in just interest.
We are told that "the annual income from these investments is $900" therefore
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 Replace every copy of 'y' with '8000-x' (this works because )
Now we solve for x
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Then we use this value of x to find y
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Summary:
$3,000 was invested at 10%
$5,000 was invested at 12%
Note: if you are unsure of what and mean together in the real world, look back up at the "let" statements.
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