To solve the problem of determining how many miles a motorcycle can travel given different amounts of gas, we'll refer to the unit rate, which is 48 miles per gallon. This means that for every gallon of gas, the motorcycle can travel 48 miles.
Given the different amounts of gas, let's calculate the miles traveled for each amount:
1. For [tex]\( a \)[/tex] gallons:
- The unit rate is 48 miles per gallon.
- If [tex]\( a = 1 \)[/tex] gallon, then the motorcycle can travel:
[tex]\[
\text{miles\_a} = 1 \text{ gallon} \times 48 \text{ miles per gallon} = 48 \text{ miles}
\][/tex]
Therefore, [tex]\( \text{miles\_a} = 48 \text{ miles} \)[/tex].
2. For [tex]\( b \)[/tex] gallons:
- Again, the unit rate is 48 miles per gallon.
- If [tex]\( b = 2 \)[/tex] gallons, then the motorcycle can travel:
[tex]\[
\text{miles\_b} = 2 \text{ gallons} \times 48 \text{ miles per gallon} = 96 \text{ miles}
\][/tex]
Therefore, [tex]\( \text{miles\_b} = 96 \text{ miles} \)[/tex].
3. For [tex]\( c \)[/tex] gallons:
- Similarly, using the unit rate of 48 miles per gallon,
- If [tex]\( c = 3 \)[/tex] gallons, then the motorcycle can travel:
[tex]\[
\text{miles\_c} = 3 \text{ gallons} \times 48 \text{ miles per gallon} = 144 \text{ miles}
\][/tex]
Therefore, [tex]\( \text{miles\_c} = 144 \text{ miles} \)[/tex].
Thus, using the unit rate of 48 miles per gallon, the completed table for the miles traveled by a motorcycle is:
[tex]\[
\begin{array}{l}
a = 48 \text{ miles}\\
b = 96 \text{ miles}\\
c = 144 \text{ miles}
\end{array}
\][/tex]
