First, let's define the variables given in the problem:
- [tex]\( y \)[/tex] represents the total amount of gasoline in the tank after adding more gas.
- [tex]\( x \)[/tex] represents the number of gallons of gas that Jayne put into the tank.
We also know the initial amount of gas in the tank, which is 4 gallons.
### Step-by-Step Solution
1. Identify the Initial Amount of Gas:
Jayne’s tank initially has 4 gallons of gas.
2. Introduce the Variable for Additional Gas:
Let [tex]\( x \)[/tex] be the number of gallons of gas that Jayne adds to the tank.
3. Express the Total Gasoline [tex]\( y \)[/tex]:
The total gasoline in the tank, [tex]\( y \)[/tex], will be the initial amount plus the additional amount she puts in.
To find the equation that relates the total amount of gasoline [tex]\( y \)[/tex] to the number of gallons added [tex]\( x \)[/tex], we add the initial amount of gas (4 gallons) to the amount added ([tex]\( x \)[/tex] gallons).
Thus, the equation is:
[tex]\[ y = 4 + x \][/tex]
Therefore, the correct equation that relates the total amount of gasoline in the tank, [tex]\( y \)[/tex], to the number of gallons that she put in the tank, [tex]\( x \)[/tex], is:
[tex]\[ y = 4 + x \][/tex]
So, the answer is:
[tex]\[ y = 4 + x \][/tex]
Given the choices:
- [tex]\( y = 4 + x \)[/tex]
- [tex]\( y = x - 4 \)[/tex]
- [tex]\( y = 4 \cdot x \)[/tex]
- [tex]\( y = x \div 4 \)[/tex]
The correct choice is:
[tex]\[ y = 4 + x \][/tex]
