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!!!

Question

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!!!

anonymous · Answer

attachment

pooja195 · Answer

LOL

anonymous · Answer

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

anonymous · Answer

live the hug life

pooja195 · Answer

How bout u post the problem ???

steve816 · Answer

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 · Answer

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

pooja195 · Answer

Let x = amount loaned at 16%.

anonymous · Answer

would write 
"let $x$ be the amount lent at 16%"

anonymous · Answer

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

anonymous · Answer

hint, your answer has to have an x in it

steve816 · Answer

Ummm,  do I create a new variable???

anonymous · Answer

no

steve816 · Answer

D: This doesn't make sense to me

anonymous · Answer

use one , it is easier

anonymous · Answer

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

steve816 · Answer

Oh! would it be 400,000 - x

anonymous · Answer

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

steve816 · Answer

Wait, where the the 400,000 come from?

anonymous · Answer

i made it up

anonymous · Answer

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 · Answer

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

anonymous · Answer

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 · Answer

Oooooh, yes that makes sense.

anonymous · Answer

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 · Answer

600,000

anonymous · Answer

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 · Answer

1,000,000 - 20

anonymous · Answer

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 · Answer

1,000,000 - x

anonymous · Answer

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 · Answer

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

steve816 · Answer

180,000

anonymous · Answer

i believe you

anonymous · Answer

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 · Answer

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

steve816 · Answer

Yes

anonymous · Answer

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

yes it would

anonymous · Answer

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

anonymous · Answer

just put a plus sign between the two expressions

steve816 · Answer

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

anonymous · Answer

yes

anonymous · Answer

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

steve816 · Answer

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

anonymous · Answer

solve

steve816 · Answer

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

anonymous · Answer

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

steve816 · Answer

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

steve816 · Answer

Am I right?

anonymous · Answer

ikd i didn't do it

anonymous · Answer

seems right though

anonymous · Answer

yeah it is right

steve816 · Answer

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 · Answer

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