Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96. How large is her tank now?
A. 20 gallons
B. 16 gallons
C. 18 gallons
D. 14 gallons
Answer (1)
Define x as the current tank size and p as the price per gallon.
Set up the equations: x p = 42.56 and ( x + 10 ) p = 72.96 .
Solve for x by substituting p = x 42.56 into the second equation.
Calculate x = 30.4 425.6 = 14 . The current tank size is 14 gallons.
Explanation
Setting up the equations Let x be the current size of the tank in gallons, and let p be the price per gallon of gas. We are given that it costs $42.56 to fill the current tank, so we have the equation x p = 42.56 After the tank is expanded by 10 gallons, the new size of the tank is x + 10 gallons. It costs $72.96 to fill the new tank, so we have the equation ( x + 10 ) p = 72.96 We have a system of two equations with two unknowns.
Solving for x From the first equation, we can express p in terms of x :
p = x 42.56 Substitute this expression for p into the second equation: ( x + 10 ) x 42.56 = 72.96 Expand and simplify the equation: 42.56 + x 425.6 = 72.96 Subtract 42.56 from both sides: x 425.6 = 72.96 − 42.56 x 425.6 = 30.4 Multiply both sides by x :
425.6 = 30.4 x Divide both sides by 30.4: x = 30.4 425.6
Calculating the tank size Now, we calculate the value of x :
x = 30.4 425.6 = 14 Therefore, the current size of the tank is 14 gallons.
Final Answer The current size of Mrs. Hwang's gas tank is 14 gallons.
Examples
Imagine you're planning a road trip and need to upgrade your car's fuel tank. Knowing how much fuel your current tank holds and the cost to fill it helps you calculate the price per gallon. If you decide to increase your tank size, you can predict the new cost to fill it, helping you budget for the trip and decide if the upgrade is worth the investment. This kind of calculation is also useful for businesses managing fleets of vehicles, optimizing fuel costs, and planning logistics efficiently.
