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?

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

call the amount of 50% solution x and then the amount of 36% solution is 100-x

- anonymous

oops
let me start again. call the amount of 50% solution x and the amount of 24% solution is then 100-x

- anonymous

so
\[.5x+.24(100-x)=.36\times 100=36\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- 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

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

rather
\[.5x+.24y=36\]

- anonymous

Ah i see (:

- anonymous

So then...

- anonymous

it doesn't say to solve them does it?

- anonymous

x+y = 100
.24x + .5y = .36 * 100

- 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

if you want to solve it a systems you have
\[x+y=100\]
\[.5x+.24y=36\]

- anonymous

multiply the bottom equation by -2 and the x's will drop out

- anonymous

\[x+y=100\]
\[-x-.48y=-72\]

- anonymous

dude, thats weird. let y = 100 - x and substitute that into the second equation,

- 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

Naw he is doing elimination, thats substitution... i suck at substitution.. so go ahead and do elimination.. lol

- anonymous

i did that first.

- anonymous

Okay (:

- 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

unless my arithmetic is wrong. i got two ugly decimal answer. it is 50%, 24% and 36% yes?

- anonymous

oh ok

- anonymous

i trust your work , but first you want to multiply both sides to remove the decimal, if youre doing elimination

- anonymous

for the second equation, multiply both sides by 100 first

- anonymous

you try it and see if you don't get something ugly. maybe i made a mistake. really please try it.

- anonymous

ok

- anonymous

still get
\[x=\frac{12}{.26}=\frac{1200}{26}=46.153846...\]

- anonymous

sat, bear with me, im tutoring 3 other people, sorry

- anonymous

Oh yea! ^^ i think you said something about being a online tutor for money or something :P Continue though satellite (:

- anonymous

and they COMPLAIN, lol

- anonymous

yes real coin

- anonymous

They people your tutoring? Haha

- anonymous

You must be making bank....
lmfao.. kidding (:

- anonymous

yup

- anonymous

not really, im working like a dog

- anonymous

Wow... i sure cant wait to get done with high school..... :P lol

- anonymous

So i can go on to work like a dog... and make no money... sounds wonderful :P lol

- anonymous

still get x=46.15 rounded making y = 53.85 rounded

- anonymous

Okay (: Thanks!

- anonymous

welcome

- anonymous

why are you doing this and also \[b^0\] at the same time? odd

- anonymous

Haha i am retaking stuff i learned at the begining of the year :P I seriously barely remember anything. lol

- anonymous

good luck. it will be over soon enuf

- anonymous

Ya i sure hope so :P At least i got this cite tho! ^^

- anonymous

what is b^0 ?

- anonymous

Idk how to explain it... ^_T just know im doing it :P I bet satellite can tho (:

- anonymous

wait, he said youre "taking" b^0

- anonymous

Haha no its just something him and i think its polpak showed me how to do.

- anonymous

Lilly allen sucks,

Looking for something else?

Not the answer you are looking for? Search for more explanations.