Barrels

Peter has 42 barrels. One-sixth of them are filled with lemonade, one third is filled with wine and half is empty. Calculate how many barrels are with each filling.

Result

a =  7
b =  14
c =  21

Solution:

n=42 a=16 n=16 42=7n=42 \ \\ a=\dfrac{ 1 }{ 6 } \cdot \ n=\dfrac{ 1 }{ 6 } \cdot \ 42=7
b=13 n=13 42=14b=\dfrac{ 1 }{ 3 } \cdot \ n=\dfrac{ 1 }{ 3 } \cdot \ 42=14
c=12 n=12 42=21 x=16+13+12=1c=\dfrac{ 1 }{ 2 } \cdot \ n=\dfrac{ 1 }{ 2 } \cdot \ 42=21 \ \\ x=\dfrac{ 1 }{ 6 } + \dfrac{ 1 }{ 3 } + \dfrac{ 1 }{ 2 }=1



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