Let's determine how many miles the car can travel on 7 gallons of gas step-by-step.
1. Step 1: Calculate miles per gallon
- We know the car traveled 63 miles using 3 gallons of gas.
- To find miles per gallon, we divide the miles by the gallons:
[tex]\[
\text{Miles per gallon} = \frac{63 \text{ miles}}{3 \text{ gallons}} = 21 \text{ miles per gallon}
\][/tex]
2. Step 2: Determine miles traveled on 7 gallons of gas
- Next, if we have 7 gallons of gas, we want to find out how many miles the car can travel.
- We multiply the miles per gallon by the number of gallons:
[tex]\[
21 \text{ miles per gallon} \times 7 \text{ gallons} = 147 \text{ miles}
\][/tex]
3. Step 3: Setting up the proportion
- We are asked to determine the correct proportion among the given options. The relationship that correctly represents our calculations above is:
[tex]\[
\frac{63 \text{ miles}}{3 \text{ gallons}} = \frac{147 \text{ miles}}{7 \text{ gallons}}
\][/tex]
- Simplifying the proportion, we have:
[tex]\[
\frac{21 \text{ miles per gallon}} = \frac{21 \text{ miles per gallon}}
\][/tex]
- Thus, verifying the given proportions, we find the correct one matches:
[tex]\[
\frac{63}{3} = \frac{147}{7}
\][/tex]
4. Step 4: Matching with given options
- Now, let's compare this with the given options:
- [tex]\(\frac{3}{63} = \frac{m}{7} \)[/tex] is incorrect.
- [tex]\(\frac{7}{63} = \frac{m}{3} \)[/tex] is incorrect.
- [tex]\(\frac{63}{3} = \frac{m}{7} \)[/tex] is correct.
- [tex]\(\frac{83}{7} = \frac{m}{3} \)[/tex] is incorrect.
Hence, the correct proportion to determine how many miles [tex]\( m \)[/tex] the car can travel on 7 gallons of gas is:
[tex]\[
\boxed{\frac{63}{3} = \frac{m}{7}}
\][/tex]
