24carat gold

The goldsmith cast 22-carat gold and 14-carat gold and earned 20 dkg of 18-carat gold. How much gold did he use?

Correct answer:

a =  10 dkg
b =  10 dkg

Step-by-step explanation:

m=20 dkg  a+b=m 22/24⋅ a+14/24⋅ b=18/24⋅ m a+b=20 22/24⋅ a+14/24⋅ b=18/24⋅ 20  a+b=20 22a+14b=360  Pivot:Row1↔Row2 22a+14b=360 a+b=20  Row2−221​⋅ Row1→Row2 22a+14b=360 0.36b=3.64  b=0.363636363.63636364​=10 a=22360−14b​=22360−14⋅ 10​=10=10 dkg  a=10 b=10

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