Question

How many milliliters of the 0.5% solution must be added to the 2% solution to get a 0.65% solution?

Answer 1

Use the rational function:
\[y = \frac{ (100)(0.02) + x(0.005) }{ 100 + x }\]

Answer 2

This makes my head hurt XD

Answer 3

This problem is very common in homeworks. Most of the time volume or mass is used as the parameter of interest, in this case it is volume. What you want to do is, in this case, assume you have 100mL of 2% solution, and you want to add just enough 0.5% solution to it so that the new solution is a 0.65% solution. In your case, y = 0.65, and x would be the amount of 0.5% solution you would add to make your solution 0.65%.

Answer 4

Okay, well how exactly would I start ? I know that my y = the function above and y2 would equal 0.0065 correct? It tells me I need to graph it to find x (which would be where they intersect) but everytime I do, there is no intersection

Answer 5

@Aeronautix

Answer 6

How many mL of 0.5% solution are you starting out with?

Answer 7

I don't know

Answer 8

Same

Answer 9

There is an example of how to do this problem in my textbook and it says to use the rational function given and to graph the function and whatever y2 is and where ever the intersection is would be the answer. Thats how they did it

Answer 10

You try a calc.??

Answer 11

Yes, I used a graphing calculator like they said and there is no point that I see where they intersect

Answer 12

Oh I see. There are an infinite number of combinations of volume that will give you a 0.65% solution. You must know how much of one solution you start out with. Mmmm, are you sure they don't specify a starting volume? Ok, so I guess assume the starting volume of 0.5% solution is x_1 and the volume you need from the 2% solution is x_2. Replace y with 0.0065, the solution you want to make, and 100 with x_1, the starting volume of 0.5% solution (which we will call a variable for now).

Answer 13

Oh I know what your doing now

Answer 14

The only information I know for this problem is what I posted

Answer 15

That cant be right? Unless...hold on.

Answer 16

It tells me just to graph the rational function, which I posted above and y2 whch would be 0.65% but transforming that into a decimal, not a percentage, and where the two points meet is the answer

Answer 17

The solution to this problem is a rewritten form of the equation you posted: http://www.wolframalpha.com/input/?i=0.0065%3D%28x*0.02%2By*0.005%29%2F%28x%2By%29 The volume of 0.5% solution you need (let's call this x) to add to the unknown volume of 2% solution you have (let's call this y) is a volume that will depend on the volume of 2% solution you start out with, which is a variable since we don't know how much we have to start with. So you would need, according to WolframAlpha, 9 times as much volume of 2% solution you start out with.

Answer 18

I'm not sure what your textbook is referring to when it asks for an intersection. :\

Answer 19

Sorry, with lack of book Aeronautix and i can only go so far with this.

Answer 20

I wish I knew how to show what I am seeing because I have an online textbook

Answer 21

If you graph

y1 = (100*0.02+0.005x)/(100+x)

and

y2 = 0.0065


you won't be able to see both lines using the standard window view

Answer 22

so you'll have to change your window

Answer 23

How do you change the window?

Answer 24

if you make

xmin = 600
xmax = 1200
ymin = -0.006
ymax = 0.012

then you should have a better view of both lines (and the point of intersection)

Answer 25

what kind of calculator do you have?

Answer 26

if you're using a TI-83, then you would hit the "window" button next to the "y=" button at the top

then make the proper changes

Answer 27

@Aeronautix I know how the answer for the problem, I just don't know how to show the work

Answer 28

I don't own a graphing calculator so I just use one that is online

Answer 29

which one do you use online?

Answer 30

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Answer 31

click settings

Answer 32

in there you'll be able to change your window

Answer 33

Okay, but there is also a place where you can check for intersection and since that is what I am looking for I clicked on it and it tells me that there is no intersection

Answer 34

I don't know if maybe I am putting in 0.65% in wrong or what. I put it as 0.0065, is that correct?

Answer 35

Hmm, you should think of getting a graphing calculator, it's an essential tool for doing math. Here i guess is a graphical solution, by plotting the two equations (you'd see the two equations at the top): http://www.wolframalpha.com/input/?i=y%3D%28%28100%29%280.02%29%2Bx%280.005%29%29%2F%28100%2Bx%29%2C+y%3D0.0065 --> 900mL of 0.5% solution for 100mL of 2% solution.

Answer 36

0.0065 is correct.

Answer 37

@Aeronautix Yes, that is what I needed because 900 mL is correct

Answer 38

take a look at this screenshot and it should all work out

Answer 39

I'm not sure though how it came up for you when I put it in the same way :/

Answer 40

Ok.

Answer 41

@jim_thompson5910 Maybe I somehow put it in wrong, but I do see the intersection on your half

Answer 42

I don't like this calculator. The x-axis is all messed up and I don't know why, but it does figure out the correct intersection point

Answer 43

Personally, I prefer geogebra because you have more control over it and can do a ton more with it

Answer 44

I was just looking for a graphing calculator online for this problem because I have one on my phone which works really well but for this type of problem it just wasn't working out so I had to find another one

Answer 45

@Aeronautix @jim_thompson5910 thank you for your help, It really helped a lot

Answer 46

Your welcome! I prefer WolframAlpha for all my college needs.

Answer 47

If you can, download geogebra because it's definitely a better graphing program

Let me know if you need help with that

Answer 48

Once you have geogebra, it's also easier to send graphs just as you see them

Answer 49

Okay thanks, I'll go and download it right now

Answer 50

ok tell me when you get it and have it running

then I'll post the graph I got

Answer 51

Okay, It is downloading right now

Answer 52

alright great

Answer 53

Okay, its all ready

Answer 54

ok here is the graph I got (see attached)

Answer 55

the red curve is the graph of y = (100*0.02+0.005x)/(100+x)

the blue line is the graph of y = 0.0065

Answer 56

I got it, thank you!

Answer 57

you're welcome

Answer 58

feel free to ask any questions you have about geogebra

it should be pretty straight forward, but you never know when you might get stuck

Answer 59

Alright, thank you so much for your help!

Answer 60

sure thing