please show me how this is done

Question

by weight, the ratio of chlorine to sodium in a salt is 54.41 to 30.00. How much sodium is contained in 56.00kg of salt?

Answer 1

The ratio is describing the weight of chlorine in relation to the weight of sodium.

If there is 54.41kg of chlorine there will also be 30kg of sodium.

54.41 + 30 = 84.41kg

For every 84.41kg of salt there will be 30kg of sodium. --> 30kg Sodium per 84.41kg Salt

 

56kg Salt (30kg Sodium/84.41kg Salt) = 19.90kg Sodium

*cross cancel the kg Salt units.

Answer 2

let x = kg of sodium

then 56.00 - x is kg of chlorine

 

the ratio of sodium to chlorine must equal 30.00/54.41

 

Therefore 30.00/54.41 = x /(56-x)

 

30(56-x) = 54.41x

 

1680 - 30x = 54.41x

 

1680 = 84.41x

 

x = 1680/84.41 = 19.90 kg