SOLUTION: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term-growth supplement and 50 pounds of weed killer. The new packa
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Question 1178545: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term-growth supplement and 50 pounds of weed killer. The new packages contain 45 pounds of long-term-growth supplement and 65 pounds of weed killer. Using past experience, the farmer estimates that he needs 3900 pounds of long-term-growth supplement and 4350 pounds of weed killer for the fields. How many old packages of fertilizer and how many new packages of fertilizer should he use?
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A farmer has several packages of fertilizer for his new grain crop.
The old packages contain 60 pounds of long-term-growth supplement and 50 pounds of weed killer.
The new packages contain 45 pounds of long-term-growth supplement and 65 pounds of weed killer.
Using past experience, the farmer estimates that he needs 3900 pounds of long-term-growth supplement and 4350 pounds of weed killer for the fields.
How many old packages of fertilizer and how many new packages of fertilizer should he use?
:
Let a = no. of old fertilizer bags
Let b = no. of new
:
60a + 45b = 3900, amt of long term sup
50a + 65b = 4350, amt of weed killer sup
:
We can simplify these equations, divide the 1st by 60, the 2nd by 50
a + .75b = 65
a + 1.3b = 87
---------------subtraction eliminates a, find b
0 - .55b = -22
b = -22/-.55
b = +40 bags of the new stuff
:
Find a;
a + .75(40) = 65
a + 30 = 65
a = 65 - 30
a = 35 bags of the old stuff
:
:
Check this in original 1st equation
60(35) + 45(40) =
2100 + 1800 = 3900
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