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Discussion Starter · #1 ·
My son, daughter and I are all sitting here stewing over this.

Solution A is 20% acid.
Solution B is 50% acid.

How much of solution A and B do you need to mix together to come up with 90 mL of solution that is 40% acid?

Anyone? Please explain your work, too. Thanks!

L
 

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Sorry. . . .only took one semester of Chem in college and I don't remember how to do that sort of problem.  Best I can do is tell you it looks like you'll need more of B than A.  :D
 

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Leslie said:
My son, daughter and I are all sitting here stewing over this.

Solution A is 20% acid.
Solution B is 50% acid.

How much of solution A and B do you need to mix together to come up with 90 mL of solution that is 40% acid?

Anyone? Please explain your work, too. Thanks!

L
Okay we know that A + B = 90 mL

So B = 90 - A

Now we also know that A times the .2 solution plus B times the .5 solution needs to yield 90 mL of the .4 solution -- so

A(.2) + B(.5) = 90 (.4)

And if we substitute from above this becomes

A(.2) + (90-A)(.5) = 90(.4)

Multiplying everything out

.2A + 45 - .5A = 36

Simplifying

45 - .3A = 36

Solve for A

45-36=.3A
9=.3A
30=A

If A = 30 then B=90-A or B=90-30 or B=60

So you need 30 mL of 20% acid plus 60 mL of 50% acid to yield 90 mL of 40% acid
 

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Gah!  I was playing with it and trying to think algebraically. . . .had just gotten there when I saw this!  :D
 

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Discussion Starter · #5 ·
Tip...THANK YOU! Now we can all stop going bananas.

We basically had everything except we forgot the very first step you listed:

So B = 90 - A
and so we kept getting stumped because we had two variables (x, y) and couldn't figure out the equation!

THANK YOU AGAIN...my son can leave for camp a happy man and I can explain the problem to my daughter when she gets home.

L
 

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No problem Leslie -- it was a fun exercise, I enjoyed it. 
It provided a nice bump start to my day.

 

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Just because I'm bored, here's a brute force programmatic solution (in PHP) that validates the (much better) algebraic solution:
Code:
<?php
$found = false;
for($x=0, $y=90; $x <= 90; $x+=1, $y-=1)
{
   if(0.2 * $x + 0.5 * $y == 0.4 * 90)
   {
      $found = true;
      echo "Use {$x}mL of 20% solution and {$y}mL of 50% solution.";
      break;
   }
}
if(!$found)
{
   echo "Solution not found: maybe it's not an integral amount?";
}
Output:
Use 30mL of 20% solution and 60mL of 50% solution.
;D
 

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What a way to start a Friday morning, at least it was not a  Monday morning exercise  :mad:
 

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Thumper said:
Math is hard.
NOPE Math is EASY -- WRITING is Hard!

Guess its all in how we're wired huh? Thump!

Your write very good stories but think math is hard.
I think math is easy but couldn't write a decent story to save my soul.

Thank God for Diversity. Be a boring world otherwise! ;)
 

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I should NOT have opened this thread at 1 a.m. My brain hurts now!
 

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I opened it at 10am, didn't help.
 
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