SOLUTION: Two boxes of groceries each have a mass of 20 kg. The mass of the first box increases to 29 kg after a bag of potatoes and 3 bags of rice are added to it. The mass of the se

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two boxes of groceries each have a mass of 20 kg. The mass of the first box increases to 29 kg after a bag of potatoes and 3 bags of rice are added to it. The mass of the se      Log On


   

Question 767820: Two boxes of groceries each have a mass of 20 kg. The mass of the first box increases to 29 kg after a
bag of potatoes and 3 bags of rice are added to it. The mass of the second box decreases to 16 kg after
2 bags of potatoes are removed and 1 bag of rice is added to it. What are the individual masses of a
bag of potatoes and a bag of rice?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Unknown variables are kg per bag of potatos, p;
and kg per bag of rice, r.

Box1:
kilograms increase 29 kg with 1 bag potatos and 3 bags rice.
29=1%2Ap%2B3%2Ar

Box2:
kilograms decrease by removal of potatos but addition of rice...
DECREASE by 16 kilograms.
-16=-2%2Ap%2B1%2Ar

Simpler and more convenient form for those equations as a system:
highlight%28-2p%2Br=-16%29 and highlight%28p%2B3r=29%29

the "-16" equation can be further handled, 2p-r=16.
Also if multiply this entire equation by 3 and then add to the "29" equation we can then directly solve for p; and then go back to either equation and solve for r.
.
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ANSWER: In fact, should find p=11 and therefore r=6 kilograms per bag.
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