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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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
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we need a variable for the amount invested at say 7% you pick it
it doesn't matter what you pick, so pick any letter you like
idk that's the problem i don't understand the question

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Other answers:

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

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