anonymous
  • anonymous
Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
call the amount of 50% solution x and then the amount of 36% solution is 100-x
anonymous
  • anonymous
oops let me start again. call the amount of 50% solution x and the amount of 24% solution is then 100-x
anonymous
  • anonymous
so \[.5x+.24(100-x)=.36\times 100=36\]

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anonymous
  • anonymous
this is what you need to solve. \[.5x+24-.24x=36\] \[.26x+24=36\] \[.26x=12\] \[x=\frac{12}{.26}=46.15\] rounded
anonymous
  • anonymous
but if i would read correctly it only says "wrote two equations" the first would be \[x+y=100\] and the second would be \[.5x+.24y=.6\]
anonymous
  • anonymous
rather \[.5x+.24y=36\]
anonymous
  • anonymous
Ah i see (:
anonymous
  • anonymous
So then...
anonymous
  • anonymous
it doesn't say to solve them does it?
anonymous
  • anonymous
x+y = 100 .24x + .5y = .36 * 100
anonymous
  • anonymous
Yea i do need to solve them. i can prolly do that on my own tho.... :P retaking assignments from the begining of the year >.< Dont remember a thing
anonymous
  • anonymous
if you want to solve it a systems you have \[x+y=100\] \[.5x+.24y=36\]
anonymous
  • anonymous
multiply the bottom equation by -2 and the x's will drop out
anonymous
  • anonymous
\[x+y=100\] \[-x-.48y=-72\]
anonymous
  • anonymous
dude, thats weird. let y = 100 - x and substitute that into the second equation,
anonymous
  • anonymous
add them and the x's drop out to get one equation in y \[.52y=28\] \[y=\frac{28}{.52}=53.846\] rounded
anonymous
  • anonymous
Naw he is doing elimination, thats substitution... i suck at substitution.. so go ahead and do elimination.. lol
anonymous
  • anonymous
i did that first.
anonymous
  • anonymous
Okay (:
anonymous
  • anonymous
cantorset first line i used 100-x for y. but what is odd is that usually these problems are cooked up to give nice integer answers. this one is not.
anonymous
  • anonymous
unless my arithmetic is wrong. i got two ugly decimal answer. it is 50%, 24% and 36% yes?
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
i trust your work , but first you want to multiply both sides to remove the decimal, if youre doing elimination
anonymous
  • anonymous
for the second equation, multiply both sides by 100 first
anonymous
  • anonymous
you try it and see if you don't get something ugly. maybe i made a mistake. really please try it.
anonymous
  • anonymous
ok
anonymous
  • anonymous
still get \[x=\frac{12}{.26}=\frac{1200}{26}=46.153846...\]
anonymous
  • anonymous
sat, bear with me, im tutoring 3 other people, sorry
anonymous
  • anonymous
Oh yea! ^^ i think you said something about being a online tutor for money or something :P Continue though satellite (:
anonymous
  • anonymous
and they COMPLAIN, lol
anonymous
  • anonymous
yes real coin
anonymous
  • anonymous
They people your tutoring? Haha
anonymous
  • anonymous
You must be making bank.... lmfao.. kidding (:
anonymous
  • anonymous
yup
anonymous
  • anonymous
not really, im working like a dog
anonymous
  • anonymous
Wow... i sure cant wait to get done with high school..... :P lol
anonymous
  • anonymous
So i can go on to work like a dog... and make no money... sounds wonderful :P lol
anonymous
  • anonymous
still get x=46.15 rounded making y = 53.85 rounded
anonymous
  • anonymous
Okay (: Thanks!
anonymous
  • anonymous
welcome
anonymous
  • anonymous
why are you doing this and also \[b^0\] at the same time? odd
anonymous
  • anonymous
Haha i am retaking stuff i learned at the begining of the year :P I seriously barely remember anything. lol
anonymous
  • anonymous
good luck. it will be over soon enuf
anonymous
  • anonymous
Ya i sure hope so :P At least i got this cite tho! ^^
anonymous
  • anonymous
what is b^0 ?
anonymous
  • anonymous
Idk how to explain it... ^_T just know im doing it :P I bet satellite can tho (:
anonymous
  • anonymous
wait, he said youre "taking" b^0
anonymous
  • anonymous
Haha no its just something him and i think its polpak showed me how to do.
anonymous
  • anonymous
Lilly allen sucks,

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