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anonymous

  • one year ago

A man invests $20,000 to yield $1,280 interest annually.If part of his investment pays 6% annually and the rest of his investment pays 7% annually,how much does he invest at each rate?

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  1. anonymous
    • one year ago
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    we need a variable for the amount invested at say 7% you pick it

  2. anonymous
    • one year ago
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    it doesn't matter what you pick, so pick any letter you like

  3. anonymous
    • one year ago
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    idk that's the problem i don't understand the question

  4. anonymous
    • one year ago
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    i will walk you through it

  5. anonymous
    • one year ago
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    we need two numbers, the amount invested at 7% and the amount invested at 6% to do a problem like this, you need to have a variable representing some number you want, then you need an equation to solve but the first step is to make a variable you pick it

  6. anonymous
    • one year ago
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    pick some letter to represent the amount invested at 7% interest

  7. anonymous
    • one year ago
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    you can pick such your smart and you know what your doing

  8. anonymous
    • one year ago
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    there are 26 letters in the alphabet, you do not need to be smart to pick one of them

  9. anonymous
    • one year ago
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    just asking are you a boy or girl?

  10. anonymous
    • one year ago
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    also there is the greek alphabet, you can pick a letter from there too the indians used colors for there variables

  11. misty1212
    • one year ago
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    HI!!

  12. misty1212
    • one year ago
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    why don't you pick \(x\) that is what the math teachers usually use

  13. anonymous
    • one year ago
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    ok \(x\) it is then if the amount invested at 7% is \(x\) and the total is \(20,000\) then the amount invested at 6% is \(20,000-x\)

  14. anonymous
    • one year ago
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    then

  15. misty1212
    • one year ago
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    7% of \(x\) is \(0.07x\) right? at 6% of \(20,,000-x\) is \(.06(20,000-x)\)

  16. anonymous
    • one year ago
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    yes, and since the total interest is 1280 you know that \[.07x+.06(20,000-x)=1280\]

  17. anonymous
    • one year ago
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    final job is to solve that for \(x\)

  18. misty1212
    • one year ago
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    yeah but decimals are so annoying

  19. anonymous
    • one year ago
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    k lets get rid of them by multiplying both sides by 100 to clear the decimals

  20. misty1212
    • one year ago
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    oh ok, then we can just solve \[7x+6(20,000-x)=128,000\]

  21. anonymous
    • one year ago
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    yeah if you multiply both sides by 100 the decimal goes, and of course you have to multiply \(1280\times 100\) to get \(128,000\)

  22. misty1212
    • one year ago
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    now it should be easy right? distribute the 6 then combine like terms then you can solve for \(x\) in one step

  23. anonymous
    • one year ago
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    so x is suppose to equal to?

  24. misty1212
    • one year ago
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    you still have to find \(x\) by solving \[7x+6(20,000-x)=128,000\]

  25. anonymous
    • one year ago
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    i mean how much does he invest at each rate?

  26. misty1212
    • one year ago
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    solve for \(x\) and you will know how much is invested at 7% do you know how to do that?

  27. anonymous
    • one year ago
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    no

  28. anonymous
    • one year ago
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    its all too confusing

  29. misty1212
    • one year ago
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    then skip it you need to know how to solve basic linear equations first before you can worry about complicated word problems

  30. anonymous
    • one year ago
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    but its homework and i need to finish it,its due tomorrow that's why i need help to find what x is

  31. terenzreignz
    • one year ago
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    Well, let's see what we can do ^^ Do you know what "distribute" means in this context? \[7x+\color{red}6(\color{blue}{20,000}-\color{green}x)=128,000\]

  32. misty1212
    • one year ago
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    it is too confusing go back and learn how to solve linear equations first then you need to know how to set up a word problem finally you can tackle something like this there is not royal road to algebra, you have to do it step by step

  33. terenzreignz
    • one year ago
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    Miss Tea scared her off D: Oh noes

  34. misty1212
    • one year ago
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    any one who starts of with "i don't get it" "this is too confusing" "this doesn't make sense" is not ready to begin a problem like this you could go ahead and give the answer, but it will make no sense at all look at all the work we did just to set up the equation need to go back and learn the basics, then we can tackle something like this

  35. terenzreignz
    • one year ago
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    Aww, there's no need to get so extreme ^^ Come on, @vickie11223 work with me here. What I want you to do is distribute the 6 to the two terms inside the parentheses. What that means is you multiply 6 to those two terms. Can you do that? \[7x+\boxed{6(20,000-x)}=128,000\] Focus on the stuff in the box first.

  36. anonymous
    • one year ago
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    yes

  37. terenzreignz
    • one year ago
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    |dw:1439057511466:dw|

  38. terenzreignz
    • one year ago
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    My handwriting is terrible, but this might give you a better idea on what "distribution" is. Multiply ^^

  39. anonymous
    • one year ago
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    120000-6x

  40. terenzreignz
    • one year ago
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    Great. So going back to the equation, we get \[\Large 7x+ \color{blue}{120000 - 6x}=128,000\] Anything you can simplify?

  41. anonymous
    • one year ago
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    minus 120,000 to 128000

  42. terenzreignz
    • one year ago
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    Not the more obvious thing to do, but sure. Just so we're clear, what will your equation look like after that?

  43. anonymous
    • one year ago
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    or minus 7x to negtive 6x

  44. terenzreignz
    • one year ago
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    Slowly, now ^^ Step by step. Show your steps. All of them. Preferably one at a time. I'll add my commentary to them XD

  45. anonymous
    • one year ago
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    i don't know would you like to show me?

  46. terenzreignz
    • one year ago
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    I would love to, but you know, you already outlined two things that you CAN do. I wanted you to show me your steps so I can make sure you're doing them correctly :D

  47. anonymous
    • one year ago
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    um 7x+8000-6x?

  48. anonymous
    • one year ago
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    ugh im so stupid

  49. terenzreignz
    • one year ago
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    Okay. This could use some work XD Remember that we're dealing with equations here, you need to have the = sign. And never ever admit to stupidity haha

  50. anonymous
    • one year ago
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    7+-6x+=8000

  51. terenzreignz
    • one year ago
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    I'd rather you showed me your steps. But... anyway, can I trust that you knew what you were doing when you got to this equation?

  52. terenzreignz
    • one year ago
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    oh and uhh you missed a spot. x's don't just disappear ;) HAHA no pun intended

  53. anonymous
    • one year ago
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    |dw:1439058198385:dw|

  54. anonymous
    • one year ago
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    is this right

  55. terenzreignz
    • one year ago
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    As a matter of fact, yes ^^ Now you got x. That's the amount invested for 7% as I recall What about the amount invested for 6%?

  56. anonymous
    • one year ago
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    can you show me the equation?

  57. terenzreignz
    • one year ago
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    no need for that, just simple logic. The bloke invested 20,000, yes? one part for 7% which is 8000 the rest has to have been invested for 6% Take 8000 from 20000, what do you have left? ^_^

  58. anonymous
    • one year ago
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    12000

  59. terenzreignz
    • one year ago
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    and there you go ^^

  60. terenzreignz
    • one year ago
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    Just to make sure, what's 6% of 12000?

  61. anonymous
    • one year ago
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    idk would youlike to help me lol

  62. terenzreignz
    • one year ago
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    Come on -_- Calculators can do that for you. haha

  63. anonymous
    • one year ago
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    hahaha i dont have one with me do you

  64. terenzreignz
    • one year ago
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    okay, to get 6% of something, multiply it by 0.06 Now, what's 6% of 12000?

  65. anonymous
    • one year ago
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    720

  66. terenzreignz
    • one year ago
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    Right. What's 7% of 8000? Multiply by 0.07 ;)

  67. anonymous
    • one year ago
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    but i need to find how much does he invest at each rate

  68. terenzreignz
    • one year ago
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    Didn't you already do that? You defined x as the amount he invested for 7% and you got... what?

  69. terenzreignz
    • one year ago
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    What is x?

  70. anonymous
    • one year ago
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    560

  71. terenzreignz
    • one year ago
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    That's 7% of 8000 lol

  72. anonymous
    • one year ago
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    8000?

  73. terenzreignz
    • one year ago
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    now add them up. 560 and 720 and you get?

  74. anonymous
    • one year ago
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    1220

  75. terenzreignz
    • one year ago
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    I don't think so?

  76. anonymous
    • one year ago
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    1280

  77. terenzreignz
    • one year ago
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    And that's exactly how much interest he was supposed to earn, as per your problem. Good job!

  78. anonymous
    • one year ago
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    but thats how much he yielded

  79. anonymous
    • one year ago
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    i need to find how much he invest at each rate

  80. terenzreignz
    • one year ago
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    I know. That was only supposed to check that your answer was correct, and it is ^^ x is how much he invested at 7% and you already got a value for x.

  81. anonymous
    • one year ago
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    which is 1280

  82. anonymous
    • one year ago
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    that is what i put as my answer

  83. terenzreignz
    • one year ago
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    no. Look back to the equation you solved. You got a value for x.

  84. anonymous
    • one year ago
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    8000

  85. terenzreignz
    • one year ago
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    That's right.

  86. anonymous
    • one year ago
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    and that is the value of x

  87. terenzreignz
    • one year ago
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    and that's how much he invested at 7%

  88. anonymous
    • one year ago
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    oh thank you your so smart

  89. anonymous
    • one year ago
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    i need help with one more question

  90. terenzreignz
    • one year ago
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    Just a little ;) Now that this is done, do in fact, follow Misty's lead and give your "solving linear equations" a thorough review.

  91. anonymous
    • one year ago
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    ;)

  92. anonymous
    • one year ago
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    i think i need a one on one tutor like you

  93. terenzreignz
    • one year ago
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    There are plenty of those. Here. They'll only be too happy to help you...sometimes all at once haha

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