SOLUTION: What quantity of 70% acid solution must be mixed with a 30 solution to produce 960 mL of a 50% solution? Please help me!

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Question 906376: What quantity of 70% acid solution must be mixed with a 30 solution to produce 960 mL of a 50% solution?
Please help me!
Found 2 solutions by Alan3354, richwmiller:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
50 is the average of 70 and 30 --> equal amounts

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor Alan is correct. He knows some neat shortcuts.
Here is the proof.
a+b=960,
0.7*a+0.3*b=0.5*960
a=960-b
0.7*(960-b)+0.3*b=480
672-0.7b+0.3*b=480
-0.4*b=-192
b=480
a=960-b
a=480 mL at 0.7% b=480 mL at 0.3%
check
0.7*480+0.3*480=0.5*960
336+144=480
480=480
ok