SOLUTION: Please help with mixture problem. I can't figure out how to get the equation. Thanks! A chemist needs 70mL of a 32% solution, but has only 26% and 47% solutions available. Find

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Question 1066435: Please help with mixture problem. I can't figure out how to get the equation. Thanks!
A chemist needs 70mL of a 32% solution, but has only 26% and 47% solutions available. Find how many mL of each that should be mixed to get the desired solution.
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Please help with mixture problem. I can't figure out how to get the equation. Thanks! 
A chemist needs 70mL of a 32% solution, but has only 26% and 
47% solutions available. Find how many mL of each that should 
be mixed to get the desired solution. 

An N% solution is some liquid which is N% pure stuff and the 
rest water.  Make this chart:

                  |  mL  |   %   |mL of
                  |  of  |  as   |pure
                  |liquid|decimal|stuff
------------------------------------------- 
Weaker solution   |   x  | 0.26  |0.26*x
Stronger solution |   y  | 0.47  |0.47*y
-------------------------------------------
Desired solution  |  70  | 0.32  |0.32*70

The equations come from the two end columns:



The second equation simplifies to

26x + 47y = 2240

solve for x and y.

Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = ml of 26% solution needed
Let = ml of 47% solution needed
--------------------------------------
(1)
(2)
----------------------------------
(2)
(2)
(2)
----------------------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
----------------------------


and
(1)
(1)
-----------------------
50 ml of 26% solution are needed
20 ml of 47% solution are needed
-------------------------------
check:
(2)
(2)
You can finish this check

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