Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, $y$, to the number of gallons that she put in the tank, $x$?
A. $y=4+x$
B. $y=x-4$
C. $y=4 \cdot x$
D. $y=x \div 4$
Answer (1)
The gas tank starts with 4 gallons.
Jayne adds x gallons.
The total amount of gas, y , is the sum of the initial amount and the added amount.
The equation is y = 4 + x .
Explanation
Problem Analysis Let's analyze the problem. Jayne's gas tank already has 4 gallons of gas. She adds x gallons, and we want to find an equation that tells us the total amount of gas, y , in the tank.
Formulating the Equation The total amount of gas, y , is the sum of the initial amount (4 gallons) and the amount Jayne adds ( x gallons). So, we can write the equation as: y = 4 + x
Final Answer Therefore, the equation that relates the total amount of gasoline in the tank, y , to the number of gallons that she put in the tank, x , is y = 4 + x .
Examples
Imagine you're filling a swimming pool that already has some water in it. If the pool initially has 4 gallons of water and you add x more gallons, the total amount of water in the pool, y , is simply the sum of the initial amount and the amount you added. This is a direct application of the equation y = 4 + x . Understanding this concept helps in many real-life scenarios where you're adding to an initial quantity.
