Help! Why do I suck at word problems so much :(
I am good with equations and stuff, but when I stare at a word problem I suffer because I don't know how to set up the equation!!!

- steve816

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- schrodinger

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- anonymous

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- pooja195

LOL

- anonymous

same. bruh you needa like rip the paper and ya thats how you do et

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## More answers

- anonymous

live the hug life

- pooja195

How bout u post the problem ???

- steve816

Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year. If she can lend at a rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?
I've been staring at this problem for half an hour and I don't even know where to start!

- anonymous

you have to start by making a variable to represent what you are trying to find
write it out (spend the ink)

- pooja195

Let x = amount loaned at 16%.

- anonymous

would write
"let \(x\) be the amount lent at 16%"

- anonymous

then since the total lent is one million, the amount lent at 19% must be what?

- anonymous

hint, your answer has to have an x in it

- steve816

Ummm, do I create a new variable???

- anonymous

no

- steve816

D: This doesn't make sense to me

- anonymous

use one , it is easier

- anonymous

ok let me ask you this
suppose you invest $400,000 at 16%
what gets invested at 19%?

- steve816

Oh! would it be 400,000 - x

- anonymous

let me ask again
the total is one million
you invest 400,000 at 16%
how much is left to invest at 19%?

- steve816

Wait, where the the 400,000 come from?

- anonymous

i made it up

- anonymous

after you do it with 400,000 we can do it with 700,000 and with 20,000 so we understand what we are doing and it is not so mysterious

- steve816

Man, this is really confusing, I feel really stupid.

- anonymous

ok i will give an example
i have a million dollars to invest (yeah right)
i invest $200,000 at 16%
that leaves me with $800,000 to invest at 19%
clear?

- steve816

Oooooh, yes that makes sense.

- anonymous

ok now your turn
you have one million to invest
you invest $400,000 at 16%
how much do you have left to invest at 19%?

- steve816

600,000

- anonymous

ok good
now another
you have one million to invest
you invest $20 at 16%
how much do you have left to invest at 19%?

- steve816

1,000,000 - 20

- anonymous

yay
now lets cut to the chase
you invest \(x\) at 16%
how much do you have left to invest at 19%?
your answer must have an x in it

- steve816

1,000,000 - x

- anonymous

ok good
in summery ( we are not done) you invest \(x\) at 16% and that leaves you \(1,000,000-x\) so invest at 19%
next...

- anonymous

you want to average 18% of the one million
what is 18% of one million?

- steve816

180,000

- anonymous

i believe you

- anonymous

ok so now how much do we make on the \(x\) dollars? 16% so we need to write 16% of x in math
that is
\[.16x\]

- anonymous

on account of 16% means 0.16 and "of" means \(\times\)
clear?

- steve816

Yes

- anonymous

ok so how much do we make on the \(1,000,000-x\) dollars invested at 19%?

- anonymous

hint, it is going to look a lot like \(.16x\) only with \(.19\) instead of \(.16\) and \(1,000,000-x\) instead of \(x\)

- steve816

ohhh, it would be .19(1,000,000 - x)

- anonymous

yes it would

- anonymous

and now we can add them up to get the total amount made

- anonymous

just put a plus sign between the two expressions

- steve816

So add the 2 expressions and make it equal to 180,000?

- anonymous

yes

- anonymous

well greater than or equal to but lets just make it equal

- steve816

.16x + .19(1,000,000 - x) = 180,000

- anonymous

solve

- steve816

Yay, now I can finish this. Setting up the equation really is the hard part for me.

- anonymous

ok
it is easier to solve by multplyying both sides by 100 and solving \[16x+19(1,000,000-x)=18,000,000\]

- steve816

16x + 19,000,000 - 19x = 18,000,000
-3x + 19,000,000 = 18,000,000
-3x = -1,000,000
x = 333,333.33

- steve816

Am I right?

- anonymous

ikd i didn't do it

- anonymous

seems right though

- anonymous

yeah it is right

- steve816

I really appreciate your help man. I have gained a little bit of confidence on word problems now! Thanks again for your time and help.

- anonymous

you are quite welcome, hope it makes it somewhat easier for you

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