Using a system of two linear equations?

Question

Solve The following:

A farmer has several packages of fertilizer for his new grain crop. The old packages contain 50 pounds of long-term-growth supplements and 60 pounds of weed killer. The new pakcages contain 65 pounds of long-term-growth supplements and 45 pounds of weed killer. Using past experience, the farmer estimates that he needs 3125 pounds of long-term-growth supplement and 2925 pounds of weed killer for the fields. How many old packages of fertilizer and how many new packages of fertilizer should he use?

Can you show the system of 2 equations and explain it in detail?

Answer 1

50o + 65n = 3125
60o + 45n = 2925

You need to know what numbers of old and new packages will provide you with the total amount of each component needed. Thus, the first equation shows the combo in terms of growth supplement, and the second equation shows it in terms of weed killer. Solving the equation set will give you the optimum numbers of old and new packages:
6(50o + 65n = 3125) 300o + 390n = 18750
-5(60o + 45n = 2925) -(300o + 225n = 14625)
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165n = 4125
n = 25

50o + 25(65) = 3125
50o + 1625 = 3125
50o = 1500
o = 30

The farmer should use 25 new packages and 30 old ones.

Answer 2

x is the number of old packages to use.
y is the number of new packages to use.

Each old package contributes 50 lbs of LTG supplements and each new package gives 65 lbs of LTG supplements, for a desired total of 3125 lbs of LTG.

50x + 65y = 3125

Each old package contributes 60 lbs of WK and each new package gives 45 lbs of WK, for a desired total of 2925 lbs.

60x + 45y = 2925

I'll leave the solution to you.