steve816
  • steve816
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!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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pooja195
  • pooja195
LOL
anonymous
  • anonymous
same. bruh you needa like rip the paper and ya thats how you do et

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anonymous
  • anonymous
live the hug life
pooja195
  • pooja195
How bout u post the problem ???
steve816
  • 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
  • anonymous
you have to start by making a variable to represent what you are trying to find write it out (spend the ink)
pooja195
  • pooja195
Let x = amount loaned at 16%.
anonymous
  • anonymous
would write "let \(x\) be the amount lent at 16%"
anonymous
  • anonymous
then since the total lent is one million, the amount lent at 19% must be what?
anonymous
  • anonymous
hint, your answer has to have an x in it
steve816
  • steve816
Ummm, do I create a new variable???
anonymous
  • anonymous
no
steve816
  • steve816
D: This doesn't make sense to me
anonymous
  • anonymous
use one , it is easier
anonymous
  • anonymous
ok let me ask you this suppose you invest $400,000 at 16% what gets invested at 19%?
steve816
  • steve816
Oh! would it be 400,000 - x
anonymous
  • 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
  • steve816
Wait, where the the 400,000 come from?
anonymous
  • anonymous
i made it up
anonymous
  • 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
  • steve816
Man, this is really confusing, I feel really stupid.
anonymous
  • 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
  • steve816
Oooooh, yes that makes sense.
anonymous
  • 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
  • steve816
600,000
anonymous
  • 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
  • steve816
1,000,000 - 20
anonymous
  • 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
  • steve816
1,000,000 - x
anonymous
  • 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
  • anonymous
you want to average 18% of the one million what is 18% of one million?
steve816
  • steve816
180,000
anonymous
  • anonymous
i believe you
anonymous
  • 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
  • anonymous
on account of 16% means 0.16 and "of" means \(\times\) clear?
steve816
  • steve816
Yes
anonymous
  • anonymous
ok so how much do we make on the \(1,000,000-x\) dollars invested at 19%?
anonymous
  • 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
  • steve816
ohhh, it would be .19(1,000,000 - x)
anonymous
  • anonymous
yes it would
anonymous
  • anonymous
and now we can add them up to get the total amount made
anonymous
  • anonymous
just put a plus sign between the two expressions
steve816
  • steve816
So add the 2 expressions and make it equal to 180,000?
anonymous
  • anonymous
yes
anonymous
  • anonymous
well greater than or equal to but lets just make it equal
steve816
  • steve816
.16x + .19(1,000,000 - x) = 180,000
anonymous
  • anonymous
solve
steve816
  • steve816
Yay, now I can finish this. Setting up the equation really is the hard part for me.
anonymous
  • 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
  • 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
  • steve816
Am I right?
anonymous
  • anonymous
ikd i didn't do it
anonymous
  • anonymous
seems right though
anonymous
  • anonymous
yeah it is right
steve816
  • 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
  • anonymous
you are quite welcome, hope it makes it somewhat easier for you

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