Sure, let's break down the problem step-by-step to find the correct equation that relates the total amount of gasoline in the tank [tex]\( y \)[/tex] to the number of gallons that Jayne added [tex]\( x \)[/tex].
1. Understand what we know:
- Jayne already had 4 gallons of gas in the tank.
- She then adds [tex]\( x \)[/tex] gallons of gas to the tank.
2. Determine the relationship between the total gasoline in the tank and the additional gasoline added:
- The total amount of gasoline [tex]\( y \)[/tex] is the sum of the gasoline already in the tank and the gasoline she added.
- Since the tank already has 4 gallons, we can say [tex]\( y = 4 \)[/tex] (initial gas) [tex]\( + x \)[/tex] (gas added).
3. Translate this relationship into an equation:
- Total gasoline [tex]\( y = 4 + x \)[/tex].
4. Evaluate the given choices:
- [tex]\( y = 4 + x \)[/tex]: This matches our equation perfectly.
- [tex]\( y = x - 4 \)[/tex]: This would mean subtracting 4 gallons from what she added, which doesn't match our situation.
- [tex]\( y = 4 \cdot x \)[/tex]: This suggests the total gasoline is the product of 4 gallons and the added gallons, which is incorrect.
- [tex]\( y = x \div 4 \)[/tex]: This would imply dividing the added gasoline by 4, which is also incorrect.
So, the correct equation that represents the relationship between the total amount of gasoline in the tank [tex]\( y \)[/tex] and the number of gallons [tex]\( x \)[/tex] that Jayne puts in the tank is:
[tex]\[ y = 4 + x \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{y = 4 + x} \][/tex]
