Question
Draw and use a double number line diagram to model and solve the given problem.
The Williams family went to the beach during summer vacation. They traveled 459 miles and used a full tank of gas, which holds 17 gallons. If the total distance to their beach destination is 594 miles, how many gallons of gas will the Williams family need?
A.
21 gallons
B.
34 gallons
C.
22 gallons
D.
23 gallons
The Williams family went to the beach during summer vacation. They traveled 459 miles and used a full tank of gas, which holds 17 gallons. If the total distance to their beach destination is 594 miles, how many gallons of gas will the Williams family need?
A.
21 gallons
B.
34 gallons
C.
22 gallons
D.
23 gallons
Answers
GPT-4o mini
To solve the problem, we can use a double number line diagram to help visualize the relationship between the distance traveled and the amount of gas used.
1. **Understanding the data**:
- Distance traveled with a full tank (459 miles) = 17 gallons
- Total distance to beach = 594 miles
2. **Calculate the miles per gallon**:
- To find the miles per gallon (mpg), we can divide the distance traveled by the gallons used:
\[
\text{mpg} = \frac{459 \text{ miles}}{17 \text{ gallons}} \approx 27 \text{ miles per gallon}
\]
3. **Setting up the double number line**:
We'll create two separate number lines: one for distance (in miles) and one for the amount of gas used (in gallons).
Let's map out the relationship using the known data points:
- **Miles**: 0 miles corresponds to 0 gallons, 459 miles corresponds to 17 gallons.
- We want to find how many gallons are needed for 594 miles.
We can represent it like this:
```
Miles: 0 459 594
|----|---|
Gallons: 0 17 ?
```
4. **Finding the required gallons for 594 miles**:
Since we know that 459 miles corresponds to 17 gallons, we will find the number of gallons needed to reach 594 miles.
We can use a proportion based on the current data:
\[
\frac{17 \text{ gallons}}{459 \text{ miles}} = \frac{x \text{ gallons}}{594 \text{ miles}}
\]
Cross-multiply to solve for \(x\):
\[
17 \cdot 594 = 459 \cdot x
\]
\[
10098 = 459x
\]
Now divide both sides by 459:
\[
x = \frac{10098}{459} \approx 22
\]
Therefore, the Williams family will need **approximately 22 gallons**.
The answer is **C. 22 gallons**.
1. **Understanding the data**:
- Distance traveled with a full tank (459 miles) = 17 gallons
- Total distance to beach = 594 miles
2. **Calculate the miles per gallon**:
- To find the miles per gallon (mpg), we can divide the distance traveled by the gallons used:
\[
\text{mpg} = \frac{459 \text{ miles}}{17 \text{ gallons}} \approx 27 \text{ miles per gallon}
\]
3. **Setting up the double number line**:
We'll create two separate number lines: one for distance (in miles) and one for the amount of gas used (in gallons).
Let's map out the relationship using the known data points:
- **Miles**: 0 miles corresponds to 0 gallons, 459 miles corresponds to 17 gallons.
- We want to find how many gallons are needed for 594 miles.
We can represent it like this:
```
Miles: 0 459 594
|----|---|
Gallons: 0 17 ?
```
4. **Finding the required gallons for 594 miles**:
Since we know that 459 miles corresponds to 17 gallons, we will find the number of gallons needed to reach 594 miles.
We can use a proportion based on the current data:
\[
\frac{17 \text{ gallons}}{459 \text{ miles}} = \frac{x \text{ gallons}}{594 \text{ miles}}
\]
Cross-multiply to solve for \(x\):
\[
17 \cdot 594 = 459 \cdot x
\]
\[
10098 = 459x
\]
Now divide both sides by 459:
\[
x = \frac{10098}{459} \approx 22
\]
Therefore, the Williams family will need **approximately 22 gallons**.
The answer is **C. 22 gallons**.