Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

this is what you need to solve.
\[.5x+24-.24x=36\]
\[.26x+24=36\]
\[.26x=12\]
\[x=\frac{12}{.26}=46.15\] rounded

Answer 5

but if i would read correctly it only says "wrote two equations"
the first would be
\[x+y=100\] and the second would be
\[.5x+.24y=.6\]

Answer 6

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

Answer 7

Ah i see (:

Answer 8

So then...

Answer 9

it doesn't say to solve them does it?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

add them and the x's drop out to get one equation in y
\[.52y=28\]
\[y=\frac{28}{.52}=53.846\] rounded

Answer 17

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

Answer 18

i did that first.

Answer 19

Okay (:

Answer 20

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.

Answer 21

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

Answer 22

oh ok

Answer 23

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

Answer 24

for the second equation, multiply both sides by 100 first

Answer 25

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

Answer 26

ok

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

and they COMPLAIN, lol

Answer 31

yes real coin

Answer 32

They people your tutoring? Haha

Answer 33

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

Answer 34

yup

Answer 35

not really, im working like a dog

Answer 36

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

Answer 37

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

Answer 38

still get x=46.15 rounded making y = 53.85 rounded

Answer 39

Okay (: Thanks!

Answer 40

welcome

Answer 41

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

Answer 42

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

Answer 43

good luck. it will be over soon enuf

Answer 44

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

Answer 45

what is b^0 ?

Answer 46

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

Answer 47

wait, he said youre "taking" b^0

Answer 48

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

Answer 49

Lilly allen sucks,