SOLUTION: A solution of 81% bleach is to be mixed with a solution of 96% bleach to make 135 L of a 87% solution. How many liters of the 81% solution must be used?

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Question 1092257:
A solution of 81%
bleach is to be mixed with a solution of 96% bleach to make 135 L of a 87% solution. How many liters of the 81% solution must be used?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 81% solution needed
Let +b+ = liters of 96% solution needed
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(1) +a+%2B+b+=+135+
(2) +%28+.81a+%2B+.96b+%29+%2F+135+=+.87+
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(2) +.81a+%2B+.96b+=+117.45+
(2) +81a+%2B+96b+=+11745+
(2) +27a+%2B+32b+=+3915+
Multiply both sides of (1) by +27+ and
subtract (1) from (2)
(2) +27a+%2B+32b+=+3915+
(1) +-27a+-+27b+-+-3645+
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+5b+=+270+
+b+=+54+
and
(1) +a+%2B+54+=+135+
(1) +a+=+81+
------------------------
81 liters of 81% solution are needed
54 liters of 96% solution are needed
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check:
(2) +%28+.81a+%2B+.96b+%29+%2F+135+=+.87+
(2) +%28+.81%2A81+%2B+.96%2A54+%29+%2F+135+=+.87+
(2) +%28+65.61+%2B+51.84+%29+%2F+135+=+.87+
(2) +117.45+=+.87%2A135+
(2) +117.45+=+117.45+
OK