Patty prepared a simple salt solution using 3 parts salt and 4 parts water. Timmy made a salt solution using 6 parts salt and 7 parts water, Whose salution is saltier?

We have to keep in mind that a solution is saltier if and only if salt has a greater proportion within solution. The following criterion is used to determine which solution is saltier:

[tex]r = \frac{n_{salt}}{n_{salt}+n_{water}}[/tex]

Where:

[tex]r[/tex] - Salt ratio, dimensionless.

[tex]n_{salt}[/tex] - Parts of salt, dimensionless.

[tex]n_{water}[/tex] - Parts of water, dimensionless.

Now, we find the salt ratios of Patty and Timmy:

Patty ([tex]n_{salt} = 3[/tex] and [tex]n_{water} = 4[/tex])

[tex]r_{P} = \frac{3}{3+4}[/tex]

[tex]r_{P} = \frac{3}{7}[/tex]

[tex]r_{P} = 0.429[/tex]

Timmy ([tex]n_{salt} = 6[/tex] and [tex]n_{water} = 7[/tex])

[tex]r_{T} = \frac{6}{6+7}[/tex]

[tex]r_{T}= \frac{6}{13}[/tex]

[tex]r_{T} = 0.462[/tex]

The solution of Timmy is saltier.