1. Determine the chemical formula of potassium sulfide:

* Potassium (K) is in group 1, so it has a +1 charge.

* Sulfur (S) is in group 16, so it has a -2 charge.

* To balance the charges, we need two potassium ions for every sulfur ion.

* Therefore, the chemical formula for potassium sulfide is K₂S.

2. Identify the metal-to-nonmetal ratio:

* The ratio of potassium ions (metal) to sulfide ions (nonmetal) is 2:1.

3. Find another substance with the same ratio:

We need to find a compound with a 2:1 ratio of metal ions to nonmetal ions. Here are a few examples:

* Calcium Oxide (CaO): Calcium (Ca) is a metal with a +2 charge, and Oxygen (O) is a nonmetal with a -2 charge. This gives a 1:1 ratio, not what we're looking for.

* Magnesium Chloride (MgCl₂): Magnesium (Mg) is a metal with a +2 charge, and Chlorine (Cl) is a nonmetal with a -1 charge. This gives a 1:2 ratio, not what we're looking for.

* Sodium Oxide (Na₂O): Sodium (Na) is a metal with a +1 charge, and Oxygen (O) is a nonmetal with a -2 charge. This gives a 2:1 ratio, matching potassium sulfide!

Therefore, sodium oxide (Na₂O) has the same ratio of metal ions to nonmetal ions as potassium sulfide (K₂S).