Solving a mixture problem

[holmes1172]

So, I am stuck on this particular problem. The example I am given seems to have to work with than the exercise problem I am doing and it's confusing me a bit. I need to find out how much the 5% solution I need to mix with the 60mL of 20% to get the 10% solution.
5%=x
20%=60
10%=x-60

Now, if I take x+60=x+60, do I multiply 60x=x+60? or 60x=60x? Terribly lost on this one...

 

[stapel]

I need to find out how much the 5% solution I need to mix with the 60mL of 20% to get the 10% solution.

To learn how to set up and solve this sort of exercise, try here.

 

[holmes1172]

60 : 20
x : 5
======
60+x : 10

(20 * 60 + 5x) / (60 + x) = 10

Solve for x ..... let's see your solving powers, Sherlock

Well, the example in my book is not helping one itty bitty bit. I'm going to take a stab at this and at least try.

From the equation above I would move to:

(1200 + 5x) / (60 + x) = 10

Now, from here (even though we're diving) I kind of feel like I should subtract(?) stuck.

 

[Deleted member 4993]

Well, the example in my book is not helping one itty bitty bit. I'm going to take a stab at this and at least try.

From the equation above I would move to:

(1200 + 5x) / (60 + x) = 10 → 1200 + 5x = 10*(60+x)

Now, from here (even though we're diving) I kind of feel like I should subtract(?) stuck.

.

 

[Dale10101]

What's happening?

So, I am stuck on this particular problem. The example I am given seems to have to work with than the exercise problem I am doing and it's confusing me a bit. I need to find out how much the 5% solution I need to mix with the 60mL of 20% to get the 10% solution.
5%=x
20%=60
10%=x-60

Now, if I take x+60=x+60, do I multiply 60x=x+60? or 60x=60x? Terribly lost on this one...

x = # of ml of 5% solution
y = 60 ml of 20% solution
z = # of ml of 10% solution

x + y = z (Why? Because the total volume z is equal to the sum of the two volumes, x and y mixed together.)
x + 60 =z

The amount of solute (dissolved salt) in z is the sum of the solute contributed by x and y, so
.05x + .2y = .1z

Do you follow that?

overall

x + 60 = z
.05x +.2(60) = .1z

Two equations, two unknowns, not sure if you know how to solve simultaneous linear equations.

 

[stapel]

Well, the example in my book is not helping one itty bitty bit. I'm going to take a stab at this and at least try.

How about the set-up you were provided in the first reply (above) and the lesson at the link you were provided in the second reply (above)? Did you review them at all, after not finding the book's example to be helpful?

 

[holmes1172]

How about the set-up you were provided in the first reply (above) and the lesson at the link you were provided in the second reply (above)? Did you review them at all, after not finding the book's example to be helpful?

Yes, I did, once I saw your response which I hadn't at the time your posted it. I found it very helpful. Thank you.