SOLUTION: Scott's Winterizer Lawn Fertilizer is 22% nitrogen. Schultz's Lime with Lawn Fertilizer is 4% nitrogen. William Weaver, owner of Weaver's Nursery, wishes to mix these two fertilize

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Question 725240: Scott's Winterizer Lawn Fertilizer is 22% nitrogen. Schultz's Lime with Lawn Fertilizer is 4% nitrogen. William Weaver, owner of Weaver's Nursery, wishes to mix these two fertilizers to make 400 pounds of a special 10% nitrogen mixture for midseason lawn feeding. How much of each fertilizer should he mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of 22% fertilizer needed
Let +b+ = pounds of 4% fertilizer needed
given:
(1) +a+%2B+b+=+400+
(2) +%28+.22a+%2B+.04b+%29+%2F+400+=+.1+
-----------------------------
(2) +.22a+%2B+.04b+=+.1%2A400+
(2) +22a+%2B+4b+=+4000+
(2) +11a+%2B+2b+=+2000+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +11a+%2B+2b+=+2000+
(1) +-2a+-+2b+=+-800+
+9a+=+1200+
+a+=+133.33+
and
(1) +a+%2B+b+=+400+
+b+=+266.67+
133.33 pounds of 22% fertilizer are needed
266.67 pounds of 4% fertilizer are needed
check:
(2) +%28+.22a+%2B+.04b+%29+%2F+400+=+.1+
(2) +%28+.22%2A133.33+%2B+.04%2A266.67+%29+%2F+400+=+.1+
(2) +%28+29.3326+%2B+10.6668+%29+%2F+400+=+.1+
(2) +29.3326+%2B+10.6668+=+40+
(2) +39.9994+=+40+
close enough