## anonymous 5 years ago 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?

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. 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 $.5x+.24y=.6$

6. anonymous

rather $.5x+.24y=36$

7. anonymous

Ah i see (:

8. anonymous

So then...

9. anonymous

it doesn't say to solve them does it?

10. anonymous

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

11. 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

12. anonymous

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

13. anonymous

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

14. anonymous

$x+y=100$ $-x-.48y=-72$

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. anonymous

i did that first.

19. anonymous

Okay (:

20. 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.

21. anonymous

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

22. anonymous

oh ok

23. anonymous

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

24. anonymous

for the second equation, multiply both sides by 100 first

25. anonymous

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

26. anonymous

ok

27. anonymous

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

28. anonymous

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

29. anonymous

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

30. anonymous

and they COMPLAIN, lol

31. anonymous

yes real coin

32. anonymous

33. anonymous

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

34. anonymous

yup

35. anonymous

not really, im working like a dog

36. anonymous

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

37. anonymous

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

38. anonymous

still get x=46.15 rounded making y = 53.85 rounded

39. anonymous

Okay (: Thanks!

40. anonymous

welcome

41. anonymous

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

42. anonymous

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

43. anonymous

good luck. it will be over soon enuf

44. anonymous

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

45. anonymous

what is b^0 ?

46. anonymous

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

47. anonymous

wait, he said youre "taking" b^0

48. anonymous

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

49. anonymous

Lilly allen sucks,