1. **State the problem:** We need to find an equation that models the relationship between the cost $c$ in dollars and the number of gallons $g$ of gasoline Allen buys, given that the cost is proportional to the gallons. 2. **Understand proportional relationships:** When two quantities are proportional, their ratio is constant. This means: $$ \frac{c}{g} = k $$ where $k$ is the constant of proportionality. 3. **Find the constant of proportionality $k$:** Using the given data, for example when $g=1$, $c=3$: $$ k = \frac{c}{g} = \frac{3}{1} = 3 $$ 4. **Write the equation:** Since $k=3$, the equation relating cost and gallons is: $$ c = 3g $$ 5. **Verify with other data points:** For $g=5$, $c=15$: $$ \frac{15}{5} = 3 $$ For $g=10$, $c=30$: $$ \frac{30}{10} = 3 $$ All confirm the constant $k=3$. **Final answer:** $$ c = 3g $$