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?

- anonymous

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- anonymous

we need a variable for the amount invested at say 7%
you pick it

- anonymous

it doesn't matter what you pick, so pick any letter you like

- anonymous

idk that's the problem i don't understand the question

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## More answers

- anonymous

i will walk you through it

- 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

pick some letter to represent the amount invested at 7% interest

- anonymous

you can pick such your smart and you know what your doing

- anonymous

there are 26 letters in the alphabet, you do not need to be smart to pick one of them

- anonymous

just asking are you a boy or girl?

- anonymous

also there is the greek alphabet, you can pick a letter from there too
the indians used colors for there variables

- misty1212

HI!!

- misty1212

why don't you pick \(x\) that is what the math teachers usually use

- 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

then

- misty1212

7% of \(x\) is \(0.07x\) right?
at 6% of \(20,,000-x\) is \(.06(20,000-x)\)

- anonymous

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

- anonymous

final job is to solve that for \(x\)

- misty1212

yeah but decimals are so annoying

- anonymous

k lets get rid of them by multiplying both sides by 100 to clear the decimals

- misty1212

oh ok, then we can just solve
\[7x+6(20,000-x)=128,000\]

- 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

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

- anonymous

so x is suppose to equal to?

- misty1212

you still have to find \(x\) by solving \[7x+6(20,000-x)=128,000\]

- anonymous

i mean how much does he invest at each rate?

- misty1212

solve for \(x\) and you will know how much is invested at 7%
do you know how to do that?

- anonymous

no

- anonymous

its all too confusing

- misty1212

then skip it
you need to know how to solve basic linear equations first before you can worry about complicated word problems

- 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

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

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

Miss Tea scared her off D:
Oh noes

- 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

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

yes

- terenzreignz

|dw:1439057511466:dw|

- terenzreignz

My handwriting is terrible, but this might give you a better idea on what "distribution" is.
Multiply ^^

- anonymous

120000-6x

- terenzreignz

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

- anonymous

minus 120,000 to 128000

- terenzreignz

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

- anonymous

or minus 7x to negtive 6x

- 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

i don't know would you like to show me?

- 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

um 7x+8000-6x?

- anonymous

ugh im so stupid

- 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

7+-6x+=8000

- 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

oh and uhh
you missed a spot.
x's don't just disappear ;)
HAHA no pun intended

- anonymous

|dw:1439058198385:dw|

- anonymous

is this right

- 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

can you show me the equation?

- 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

12000

- terenzreignz

and there you go ^^

- terenzreignz

Just to make sure, what's 6% of 12000?

- anonymous

idk would youlike to help me lol

- terenzreignz

Come on -_-
Calculators can do that for you. haha

- anonymous

hahaha i dont have one with me do you

- terenzreignz

okay, to get 6% of something, multiply it by 0.06
Now, what's 6% of 12000?

- anonymous

720

- terenzreignz

Right.
What's 7% of 8000?
Multiply by 0.07
;)

- anonymous

but i need to find how much does he invest at each rate

- terenzreignz

Didn't you already do that?
You defined x as the amount he invested for 7% and you got... what?

- terenzreignz

What is x?

- anonymous

560

- terenzreignz

That's 7% of 8000 lol

- anonymous

8000?

- terenzreignz

now add them up. 560 and 720 and you get?

- anonymous

1220

- terenzreignz

I don't think so?

- anonymous

1280

- terenzreignz

And that's exactly how much interest he was supposed to earn, as per your problem.
Good job!

- anonymous

but thats how much he yielded

- anonymous

i need to find how much he invest at each rate

- 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

which is 1280

- anonymous

that is what i put as my answer

- terenzreignz

no.
Look back to the equation you solved. You got a value for x.

- anonymous

8000

- terenzreignz

That's right.

- anonymous

and that is the value of x

- terenzreignz

and that's how much he invested at 7%

- anonymous

oh thank you your so smart

- anonymous

i need help with one more question

- 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

i think i need a one on one tutor like you

- 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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