1. The problem is to solve for $t$ in the proportion $\frac{16}{t} = \frac{80}{100}$.\n\n2. The formula used here is the property of proportions: if $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.\n\n3. Applying this property, we get: $$16 \times 100 = t \times 80$$\n\n4. Simplify the multiplication: $$1600 = 80t$$\n\n5. To isolate $t$, divide both sides by 80: $$\frac{1600}{\cancel{80}} = \frac{80t}{\cancel{80}}$$\n\n6. Simplify the division: $$20 = t$$\n\n7. Therefore, the solution is $t = 20$.