SOLUTION: A solution of 64% fertilizer is to be mixed with a solution of 22% fertilizer to form 84 L of a 57% solution. How many liters of the 64% solution must be used? I have a lot of ques

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Question 885821: A solution of 64% fertilizer is to be mixed with a solution of 22% fertilizer to form 84 L of a 57% solution. How many liters of the 64% solution must be used? I have a lot of questions like this on my homework and if i could just have the answer to this one and see it all worked out i could do the rest! thanks!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of the 64% fertilizer needed
Let +b+ = liters of the 22% fertilizer needed
----------------------------------------
(1) +a+%2B+b+=+84+
(2) +%28%28+.64a+%2B+.22b+%29%29+%2F+84+=+.57+
-------------------------------
(2) +.64a+%2B+.22b+=+.57%2A84+
(2) +.64a+%2B+.22b+=+47.88+
(2) +64a+%2B+22b+=+4788+
(2) +32a+%2B+11b+=+2394+
--------------------------
Multiply both sides of (1) by +32+
and subtract (2) from (1)
(1) +32a+%2B+32b+=+2688+
(2) +-32a+-+11b+=+-2394+
---------------------------
+21b+=+294+
+b+=+14+
and, since
(1) +a+%2B+b+=+84+
(1) +a+=+84+-+14+
(1) +a+=+70+
70 liters of the 64% solution are needed
-------------------------------------
check:
(2) +%28+.64a+%2B+.22b+%29+%2F+84+=+.57+
(2) +%28+.64%2A70+%2B+.22%2A14+%29+%2F+84+=+.57+
(2) +%28+44.8+%2B+3.08+%29+%2F+84+=+.57+
(2) +47.88+=+.57%2A84+
(2) +47.88+=+47.88+
OK