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I'm new to this site. I'm not sure exactly what appropriate tag I should use, but if anyone could help me with the tags, thens thats great :-) Anyways, I'm having difficulty figuring out a solution to my problem. I'm not really good with word problems so I'm not sure what type of equation I should format to get an answer. I'm not looking for the answer, I'm really looking for the equation to get my answer. I hope that makes sense. The question is below....

Michael invested $\$1,000$: one portion in a fund with 12% simple interest and the rest of money in a fund with 11% simple interest. In one year he earned $\$116$ in interest. How much was invested in each fund?

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    $\begingroup$ Step 1: understand the problem, rereading as necessary. I'll assume you've done that. Step 2: assign variables. Have you don that yet? Once you do that, Step 3 will be to translate the given information into equations with the variables. Show us your work so far. $\endgroup$
    – anon
    Commented Apr 17, 2015 at 13:31
  • $\begingroup$ That's the point, I don't understand it. I'm just stuck. $\endgroup$
    – Larry
    Commented Apr 17, 2015 at 13:32
  • $\begingroup$ What part don't you understand? Do you know what simple interest means? Maybe you aren't familiar with the words "portion" or "fund"? Be more specific. $\endgroup$
    – anon
    Commented Apr 17, 2015 at 13:33
  • $\begingroup$ Hint: you need to form 2 simultaneous equations. Let one investment be $a$ and the other be $b$. You now have $a+b=1000$ Can you find the other equation? $\endgroup$
    – Karl
    Commented Apr 17, 2015 at 13:34
  • $\begingroup$ @Larry Sorry to say this, but you are not allowed to say "I don't understand" unless you tried to solve it. Admit it or not, your problem is "I don't want bother with thinking about how to solve it" $\endgroup$
    – 5xum
    Commented Apr 17, 2015 at 13:36

3 Answers 3

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Let $A_1$ be the amount invested in the first account and let $A_2$ be the amount invested in the second account.

Thus $A_1 + A_2 = 1000$ $(1)$

Also, interest earned in the first account is:

$I_1 = 0.12*A_1$

and similarly, interest earned in the second account is:

$I_2 = 0.11A_2$

Therefore,

$0.12A_1 + 0.11A_2 = 116$ $(2)$

Equations (1) and (2) can be solved simultaneously to arrive at:

$0.01A_2 = 4$

Thus,

$A_2 = 400$ and therefore $A_1 = 600$

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  • $\begingroup$ I wish I could upvote your comment, I just don't have the privelage yet, but thank you as well. :-) $\endgroup$
    – Larry
    Commented Apr 17, 2015 at 13:42
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The answer is a=400 b=600 But you should find the way to solve this by yourself. You have great hints in the comments!

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  • $\begingroup$ Thank you, that's all I was looking for. $\endgroup$
    – Larry
    Commented Apr 17, 2015 at 13:39
  • $\begingroup$ @Larry, what about my answer, I answered first. $\endgroup$
    – Kenshin
    Commented Apr 17, 2015 at 13:39
  • $\begingroup$ @Mew cmon! Is this really important? Should i vote up your answer!? Try to help him and do not give the solution immediately. $\endgroup$
    – Al.Ka
    Commented Apr 17, 2015 at 13:40
  • $\begingroup$ @Larry Since this is an answer that tells you nothing about how to answer your question, you can hardly deny that my original comment was correct. $\endgroup$
    – 5xum
    Commented Apr 17, 2015 at 13:41
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    $\begingroup$ @5xum Did you read the part where I said two other users? Hmmm, have a good day. $\endgroup$
    – Larry
    Commented Apr 17, 2015 at 13:46
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You have to solve : $$0.12x + 0.11y = 116(1)$$ $$x+y=1000 (2)$$

Indeed, the two portions of money he invested sum up to \$1,000 $(2)$.

Simple interest basically means that if you were to invest, say, \$100 in a fund with 10% simple interest, after one year, you will have \$100 (what you invested) + 10% of \$100 (= \$10), \$110 total. You have to apply the same logic here to find $(1)$.

After calculation, you get $$x = 600, y=400$$

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