It is known that the Karat rating K of a gold object varies directly as the actual percentage P of gold in the object. A 14-Karat gold object is 58.25% gold. Wh

Question

It is known that the Karat rating K of a gold object varies directly as the actual percentage P of gold in the object. A 14-Karat gold object is 58.25% gold. What is the percentage of gold in a 16- karat object?

Answer 1

This is a proportion.

 

58.25% / 14 = x / 16

 

[ 16 ( 58.25% ) ] / 14 = x 

 

932% / 14 = x

 

66.57% = x

 

 

Answer 2

If 14K is  58.25% Au, what is 1K? One fourteenth of that. So what is 16K? Sixteen times the percent gold of 1K.

We can double check this answer. We know (do we know?) that 24 K gold is pure gold, or 100%. Is that consistent with the numbers you've used to calculate 16K? Yes, yes it is.