SOLUTION: A small bag of cement weighs x kg. A large bag of cement weighs four times as heavy as the small bag. A medium bag of cement weighs 5kg lighter than the large bag. Two small bags p

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A small bag of cement weighs x kg. A large bag of cement weighs four times as heavy as the small bag. A medium bag of cement weighs 5kg lighter than the large bag. Two small bags p      Log On


   

Question 980589: A small bag of cement weighs x kg. A large bag of cement weighs four times as heavy as the small bag. A medium bag of cement weighs 5kg lighter than the large bag. Two small bags plus a large bag weigh the same as two medium bags. Find the weight of each bag.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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S=small bag=x; M=medium bag=4x-5kg; L=large bag=4x
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2S+L=2M
2x+4x=2(4x-5kg)
6x=8x-10kg
10kg=2x
5kg=x
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S=x=5 kg ANSWER 1: The small bag weighs 5 kg.
M=4x-5kg=15 kg ANSWER 2: The medium bag weighs 15 kg.
L=4x=4(5 kg)=20 kg ANSWER 3: The large bag weighs 20 kg.
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CHECK:
Two small bags plus a large bag weigh the same as two medium bags
2S+L=2M
2(5kg)+20kg=2(15kg)
10kg+20kg=30kg
30kg=30kg