SOLUTION: A chemist has some 8% hydrogen peroxide solution and some 3% hydrogen peroxide solution, how many milliliters of each should be used to make 500-milliliter solution that is 4%?

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Question 301657: A chemist has some 8% hydrogen peroxide solution and some 3% hydrogen peroxide solution, how many milliliters of each should be used to make 500-milliliter solution that is 4%?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=500
8/100*x+3/100*y=500*4/100
x=100 y=400

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = ml of 8% solution needed
Let b = ml of 3% solution needed
given:
hydrogen peroxide in 8% solution:
.8a ml
hydrogen peroxide in 3% solution:
.3b ml
-----------------
%28.08a+%2B+.03b%29%2F500+=+.04
.08a+%2B+.03b+=+.04%2A500
.08a+%2B+.03b+=+20
(1) 8a+%2B+3b+=+2000
and
(2) a+%2B+b+=+500
Multiply both sides of (2) by 3
and subtract (2) from (1)
(1) 8a+%2B+3b+=+2000
(2) -3a+-+3b+=+-1500
5a+=+500
a+=+100
and, since
a+%2B+b+=+500
100+%2B+b+=+500
b+=+400
100 ml of 8% solution and 400 ml of 3% solution are needed
check:
.08a+%2B+.03b+=+20
.08%2A100+%2B+.03%2A400+=+20
8+%2B+12+=+20
20+=+20
OK