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Math Help - compound interest

  1. #1
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    word problem

    total interest=346.5=7500*.05 + x*.04

    solve for x.


    can you help me solve for x i got this from a word problem i had but when i get to this point lost i am.


    this is the word problem:

    A person invests $7,500 part at 5% and the remainder at 4% simple interest. If the total interest at the end of the first year was $346.50, find the amount invested at 4%.
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  2. #2
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    You haven't translated it correctly. If the 'part' is x then the 'remainder' is 7500-x. So the total interest is x*0.05 + (7500-x)*0.04 which is equal to 346.5. That is, x*0.05 + 7500*0.04 - x*0.04 = 346.5. Collecting terms, x*(0.05-0.04) + 300 = 346.5 and simplifying x*0.01 = 46.5. Now divide by 0.01 (multiply through by 100) to get x.
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  3. #3
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    i don't seem to understand this can you break it down and show your steps a little different?
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  4. #4
    Newbie Jamilworm's Avatar
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    I'll try to explain a little more. The problem indicates that the total amount the person invests is $7500. They invest part of that $7500 at 5% and the rest at 4%, so the amount invested at 5% plus the amount invested at 4% must equal $7500. The way you had it originally written out indicated that all $7500 was invested at 5% and some other amount (x) was invested at 4%. Since not all of the money is necessarily invested at 5%, you should make that amount a variable, like x. This is what rpeg was doing. If the amount that is invested at 5% is x, and the two investments must equal $7500, then the amount invested at 4% (the leftovers) is $7500 - x. Then you rewrite the equation with the amounts multiplied by the interests, giving:

    x*.05 + (7500 - x)*.04 = 346.5 (this is what rpeg wrote).

    Now you can solve for x. Hope that helps.
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