anonymous
  • anonymous
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?
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
we need a variable for the amount invested at say 7% you pick it
anonymous
  • anonymous
it doesn't matter what you pick, so pick any letter you like
anonymous
  • anonymous
idk that's the problem i don't understand the question

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More answers

anonymous
  • anonymous
i will walk you through it
anonymous
  • anonymous
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
anonymous
  • anonymous
pick some letter to represent the amount invested at 7% interest
anonymous
  • anonymous
you can pick such your smart and you know what your doing
anonymous
  • anonymous
there are 26 letters in the alphabet, you do not need to be smart to pick one of them
anonymous
  • anonymous
just asking are you a boy or girl?
anonymous
  • anonymous
also there is the greek alphabet, you can pick a letter from there too the indians used colors for there variables
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
why don't you pick \(x\) that is what the math teachers usually use
anonymous
  • anonymous
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 \(20,000-x\)
anonymous
  • anonymous
then
misty1212
  • misty1212
7% of \(x\) is \(0.07x\) right? at 6% of \(20,,000-x\) is \(.06(20,000-x)\)
anonymous
  • anonymous
yes, and since the total interest is 1280 you know that \[.07x+.06(20,000-x)=1280\]
anonymous
  • anonymous
final job is to solve that for \(x\)
misty1212
  • misty1212
yeah but decimals are so annoying
anonymous
  • anonymous
k lets get rid of them by multiplying both sides by 100 to clear the decimals
misty1212
  • misty1212
oh ok, then we can just solve \[7x+6(20,000-x)=128,000\]
anonymous
  • anonymous
yeah if you multiply both sides by 100 the decimal goes, and of course you have to multiply \(1280\times 100\) to get \(128,000\)
misty1212
  • misty1212
now it should be easy right? distribute the 6 then combine like terms then you can solve for \(x\) in one step
anonymous
  • anonymous
so x is suppose to equal to?
misty1212
  • misty1212
you still have to find \(x\) by solving \[7x+6(20,000-x)=128,000\]
anonymous
  • anonymous
i mean how much does he invest at each rate?
misty1212
  • misty1212
solve for \(x\) and you will know how much is invested at 7% do you know how to do that?
anonymous
  • anonymous
no
anonymous
  • anonymous
its all too confusing
misty1212
  • misty1212
then skip it you need to know how to solve basic linear equations first before you can worry about complicated word problems
anonymous
  • anonymous
but its homework and i need to finish it,its due tomorrow that's why i need help to find what x is
terenzreignz
  • terenzreignz
Well, let's see what we can do ^^ Do you know what "distribute" means in this context? \[7x+\color{red}6(\color{blue}{20,000}-\color{green}x)=128,000\]
misty1212
  • misty1212
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
terenzreignz
  • terenzreignz
Miss Tea scared her off D: Oh noes
misty1212
  • misty1212
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
terenzreignz
  • terenzreignz
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.
anonymous
  • anonymous
yes
terenzreignz
  • terenzreignz
|dw:1439057511466:dw|
terenzreignz
  • terenzreignz
My handwriting is terrible, but this might give you a better idea on what "distribution" is. Multiply ^^
anonymous
  • anonymous
120000-6x
terenzreignz
  • terenzreignz
Great. So going back to the equation, we get \[\Large 7x+ \color{blue}{120000 - 6x}=128,000\] Anything you can simplify?
anonymous
  • anonymous
minus 120,000 to 128000
terenzreignz
  • terenzreignz
Not the more obvious thing to do, but sure. Just so we're clear, what will your equation look like after that?
anonymous
  • anonymous
or minus 7x to negtive 6x
terenzreignz
  • terenzreignz
Slowly, now ^^ Step by step. Show your steps. All of them. Preferably one at a time. I'll add my commentary to them XD
anonymous
  • anonymous
i don't know would you like to show me?
terenzreignz
  • terenzreignz
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
anonymous
  • anonymous
um 7x+8000-6x?
anonymous
  • anonymous
ugh im so stupid
terenzreignz
  • terenzreignz
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
anonymous
  • anonymous
7+-6x+=8000
terenzreignz
  • terenzreignz
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?
terenzreignz
  • terenzreignz
oh and uhh you missed a spot. x's don't just disappear ;) HAHA no pun intended
anonymous
  • anonymous
|dw:1439058198385:dw|
anonymous
  • anonymous
is this right
terenzreignz
  • terenzreignz
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%?
anonymous
  • anonymous
can you show me the equation?
terenzreignz
  • terenzreignz
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? ^_^
anonymous
  • anonymous
12000
terenzreignz
  • terenzreignz
and there you go ^^
terenzreignz
  • terenzreignz
Just to make sure, what's 6% of 12000?
anonymous
  • anonymous
idk would youlike to help me lol
terenzreignz
  • terenzreignz
Come on -_- Calculators can do that for you. haha
anonymous
  • anonymous
hahaha i dont have one with me do you
terenzreignz
  • terenzreignz
okay, to get 6% of something, multiply it by 0.06 Now, what's 6% of 12000?
anonymous
  • anonymous
720
terenzreignz
  • terenzreignz
Right. What's 7% of 8000? Multiply by 0.07 ;)
anonymous
  • anonymous
but i need to find how much does he invest at each rate
terenzreignz
  • terenzreignz
Didn't you already do that? You defined x as the amount he invested for 7% and you got... what?
terenzreignz
  • terenzreignz
What is x?
anonymous
  • anonymous
560
terenzreignz
  • terenzreignz
That's 7% of 8000 lol
anonymous
  • anonymous
8000?
terenzreignz
  • terenzreignz
now add them up. 560 and 720 and you get?
anonymous
  • anonymous
1220
terenzreignz
  • terenzreignz
I don't think so?
anonymous
  • anonymous
1280
terenzreignz
  • terenzreignz
And that's exactly how much interest he was supposed to earn, as per your problem. Good job!
anonymous
  • anonymous
but thats how much he yielded
anonymous
  • anonymous
i need to find how much he invest at each rate
terenzreignz
  • terenzreignz
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.
anonymous
  • anonymous
which is 1280
anonymous
  • anonymous
that is what i put as my answer
terenzreignz
  • terenzreignz
no. Look back to the equation you solved. You got a value for x.
anonymous
  • anonymous
8000
terenzreignz
  • terenzreignz
That's right.
anonymous
  • anonymous
and that is the value of x
terenzreignz
  • terenzreignz
and that's how much he invested at 7%
anonymous
  • anonymous
oh thank you your so smart
anonymous
  • anonymous
i need help with one more question
terenzreignz
  • terenzreignz
Just a little ;) Now that this is done, do in fact, follow Misty's lead and give your "solving linear equations" a thorough review.
anonymous
  • anonymous
;)
anonymous
  • anonymous
i think i need a one on one tutor like you
terenzreignz
  • terenzreignz
There are plenty of those. Here. They'll only be too happy to help you...sometimes all at once haha

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