Let's determine the number of miles traveled by the motorcycle for each given amount of gas used, using the provided information that the motorcycle travels 48 miles per gallon of gas.
1. Finding the value of [tex]\(a\)[/tex]:
- Given that the motorcycle travels 48 miles per gallon, we need to find how many miles it will travel with 2 gallons of gas.
- Using the unit rate, we calculate:
[tex]\[
a = 48 \text{ miles/gallon} \times 2 \text{ gallons} = 96 \text{ miles}
\][/tex]
2. Finding the value of [tex]\(b\)[/tex]:
- Similarly, we need to find how many miles the motorcycle will travel with 3 gallons of gas.
- Using the same unit rate, we calculate:
[tex]\[
b = 48 \text{ miles/gallon} \times 3 \text{ gallons} = 144 \text{ miles}
\][/tex]
3. Finding the value of [tex]\(c\)[/tex]:
- Finally, we need to find how many miles the motorcycle will travel with 4 gallons of gas.
- Using the unit rate again, we calculate:
[tex]\[
c = 48 \text{ miles/gallon} \times 4 \text{ gallons} = 192 \text{ miles}
\][/tex]
Based on these calculations, we can now complete the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Miles Traveled & \begin{tabular}{c}
Gallons of Gas \\ Used
\end{tabular} \\
\hline
48 & 1 \\
\hline
96 & 2 \\
\hline
144 & 3 \\
\hline
192 & 4 \\
\hline
\end{tabular}
\][/tex]
Thus, the values are:
[tex]\[
a = 96, \quad b = 144, \quad c = 192
\][/tex]
