Question: Mil an is driving his motorhome. It uses $3$ gallons of gas for every $21$ miles he travels.
Complete the table below showing the number of gallons used and the distance traveled.
Number of gallons $3$ [ ] $7$ [ ] $10$
Distance (miles) $21$ $35$ [ ] $56$ [ ]
1. **State the problem:**
Mil an's motorhome uses $3$ gallons of gas for every $21$ miles. We need to complete the table showing the number of gallons used and the distance traveled, filling in the missing values.
2. **Identify the relationship:**
The problem states a proportional relationship between gallons and miles:
$$\frac{\text{gallons}}{\text{miles}} = \frac{3}{21}$$
This means for every $3$ gallons, the motorhome travels $21$ miles.
3. **Find the constant of proportionality:**
We can simplify the ratio:
$$\frac{3}{21} = \frac{\cancel{3}}{\cancel{21}} = \frac{1}{7}$$
So, $1$ gallon corresponds to $7$ miles.
4. **Complete the missing distances:**
- For $7$ gallons:
$$\text{distance} = 7 \times 7 = 49 \text{ miles}$$
- For $10$ gallons:
$$\text{distance} = 10 \times 7 = 70 \text{ miles}$$
5. **Complete the missing gallons:**
- For $35$ miles:
$$\text{gallons} = \frac{35}{7} = 5$$
- For $56$ miles:
$$\text{gallons} = \frac{56}{7} = 8$$
6. **Final completed table:**
| Number of gallons | 3 | 5 | 7 | 8 | 10 |
|-------------------|---|---|---|---|----|
| Distance (miles) | 21 | 35 | 49 | 56 | 70 |
This shows the proportional relationship clearly.
**Answer:**
- Missing gallons under $35$ miles is $5$.
- Missing gallons under $56$ miles is $8$.
- Missing distance under $7$ gallons is $49$ miles.
- Missing distance under $10$ gallons is $70$ miles.