SOLUTION: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 40 pounds of long-term growth supplement and 70 pounds of weed killer. The new packa

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Question 1154316: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 40 pounds of long-term growth supplement and 70 pounds of weed killer. The new packages contain 55 pounds of long-term growth supplement and 55 pounds of weed killer. Using past experience the farmer estimates that he needs 3125 pounds of long-term growth supplement in 4025 pounds of weed killer for the fields. How many old packages of fertilizer is and how many new packages of fertilizer should he use?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let us say he uses x old packages and y new packages.
x old packages will have
40x pounds of supplement and 70x pounds of weed killer.
y new packages will have
55y pounds of supplement and 55y pounds of weed killer.
Total supplement in the mixture should be 3125
ie 40x+%2B+55y+=+3125 --- (1)
Total weedkiller in the mixture should be 4025
ie 70x+%2B+55y+=+4025 --- (2)
We need to solve the two simultaneous equations above. Since the coefficient of y is 55 in both the equations, it makes it easy to solve!
Subtract (1) from (2) to get
70x+-+40x+%2B+55y+-+55y+=+4025+-+3125

Simplifying
30x+=+900 or x+=+30
Substituting for x in (1) we get
40%2A30+%2B+55y+=+3125 or
55y+=+3125+-+1200+=+1925 or
y+=+1925%2F55+=+35
So he needs 30 old packages and 35 new packages
Check:
30 old packages will give
30*40 supplement and 30*70 weed killer
i.e. 1200 pounds supplement and 2100 pounds weed killer
35 new packages will give
35*55 supplement and 35*55 weed killer
i.e. 1925 pounds supplement and 1925 pounds weed killer
Total supplement = 1200 + 1925 = 3125
Total weed killer = 2100 + 1925 = 4025
Check successful!
Ans: 30 old packages, 35 new packages