Let's break down the problem step by step:
1. Anju's Gasoline:
- Anju put [tex]\( 5 \frac{1}{2} \)[/tex] gallons of gasoline in her car.
- Converting this mixed number to an improper fraction gives us [tex]\( 5 \frac{1}{2} = 5.5 \)[/tex] gallons.
2. Sachit's Gasoline:
- Sachit put twice as many gallons as Anju plus 3 more gallons.
- Mathematically, this can be expressed as:
[tex]\[
\text{Sachit's gallons} = 2 \times (\text{Anju's gallons}) + 3
\][/tex]
- Substituting Anju's gallons:
[tex]\[
\text{Sachit's gallons} = 2 \times 5.5 + 3 = 11 + 3 = 14 \text{ gallons}
\][/tex]
3. Comparison:
- We need to find how many more gallons Sachit put in his car compared to Anju.
- This can be calculated by subtracting Anju's gallons from Sachit's gallons:
[tex]\[
\text{More Gas} = \text{Sachit's gallons} - \text{Anju's gallons} = 14 - 5.5 = 8.5 \text{ gallons}
\][/tex]
Now, let's evaluate the statements given in the problem:
1. In the model, A represents [tex]\(5 \frac{1}{2}\)[/tex] gallons of gas:
- True. We have established that Anju put [tex]\( 5 \frac{1}{2} \)[/tex] (5.5) gallons of gas in her car.
2. In the model, B represents the answer to the question that is being asked:
- True. The answer to the question "how many more gallons did Sachit put in his car" is represented by B, which we have calculated as 8.5 gallons.
3. Anju put more gas in her car than Sachit:
- False. Anju put 5.5 gallons, whereas Sachit put 14 gallons. Sachit put more gasoline in his car.
4. This is a comparison problem:
- True. The problem asks us to compare the amounts of gasoline put in cars by Anju and Sachit.
5. The bottom bar is three times as long as the top bar:
- False. In the bar model representation, if Anju's bar (top bar) is 5.5 units long, Sachit's bar is 14 units long, which is more than twice, but not three times as long as the top bar.
So the answers to the statements are:
- True
- True
- False
- True
- False
