SOLUTION: How much (a) water and (b) 50% soap solution must be added to one liter of a 5% soap solution to create two liters of an 8% soap solution. I'm studying for a test tomorrow, so

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Question 559912: How much (a) water and (b) 50% soap solution must be added to one liter of a 5% soap solution to create two liters of an 8% soap solution.
I'm studying for a test tomorrow, so I'm doing all the sample problems in my math book. So, no rush. Any help will be appreciated.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of water to be added
Let +b+ = liters of 50% soap solution to be added
given:
+.05%2A1+=+.05+ liters of soap in 5% solution
+.5b+ =liters of soap in 50% solution
--------------
(1) +%28+.05+%2B+.5b+%29+%2F+%28+a+%2B+b+%2B+1+%29+=+.08+
(2) +a+%2B+b+%2B+1+=+2+
--------------------
(1) +%28+.05+%2B+.5b+%29+%2F+%28+a+%2B+b+%2B+1+%29+=+.08+
(1) +.05+%2B+.5b+=+.08%2A%28+a+%2B+b+%2B+1+%29+
(1) +.05+%2B+.5b+=+.08a+%2B+.08b+%2B+.08+
(1) +.08a+-+.42b+=+-.03+
(1) +8a+-+42b+=+-3+
and
(2) +a+%2B+b+=+1+
(2) +a+=+1-+b+
and
(1) +8%2A%28+1+-+b+%29+-+42b+=+-3+
(1) +8+-+8b+-+42b+=+-3+
(1) +-50b+=+-11+
(1) +b+=+.22+
and
+a+=+1+-+.22+
+a+=+.78+
.78 liters of water and .22 liters of 50% soap
solution must be added
check answer:
(1) +%28+.05+%2B+.5%2A.22+%29+%2F+%28+.78+%2B+.22+%2B+1+%29+=+.08+
(1) +.16++%2F+2+=+.08+
(1) +.16+=+.16+
OK