SOLUTION: A farmer goes to store to buy fertilizer. Brand A bags contain 4 lbs of Sulfur and 5 lbs of nitrogen in each bag Brand B has 7 lbs of sulfur and 6 lbs of nitrogen in each bag. He n

Question 12317: A farmer goes to store to buy fertilizer. Brand A bags contain 4 lbs of Sulfur and 5 lbs of nitrogen in each bag Brand B has 7 lbs of sulfur and 6 lbs of nitrogen in each bag. He needs 308 lbs of sulfur and 330 lbs of nitrogen. How many of each brand should he get?
I think the correct answer is 42 of Brand A and 20 of Brand B. How do we solve these type of problems? Please help. I am trying to help my daughter with no luck.
Email: HKARIMI @BELLSOUTH.NET

Regards, Mike
Answer by kusha(21) (Show Source): You can put this solution on YOUR website!
Let us suppose he gets p Kg of A and q Kg of B
So he gets {4}x p of sulphur & {5}x p kg of nitro from A AND
he gets {7}x q of Sulphur & {6}x q Kg of nitro from B
Total sulphur is 4p + 7q and total nitro is 5p + 6q
But acc to ques total sulphur is 308 and total notro is 330 SO we have 2 eqns and two variables to solve . So the ques is done and only calculations remain
4p + 7q = 308 and 5p + 6q = 330
multiplying 1st eqn by 5 on both sides and 2nd by 4 on both sides we get
20p + 35q = 1540 & 20p + 24q = 1320
subtracting the two eqns 11q = 220 thus q = 20
substituting q in 1st eqn we get p = 42
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