Mrs. Hrang 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 (2)
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 dividing the equations and simplifying: x x + 10 = 42.56 72.96 .
Calculate the current tank size: x = 30.4 10 × 42.56 = 14 .
The current size of the tank is 14 gallons.
Explanation
Understanding the Problem Let's analyze the problem. We know that Mrs. Hrang's gas tank is being expanded by 10 gallons. Currently, it costs $42.56 to fill the tank. After the expansion, it will cost $72.96 to fill the tank. We need to find the current size of the tank.
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. Then we can set up two equations:
x × p = 42.56 (current cost to fill)
( x + 10 ) × p = 72.96 (cost to fill after expansion)
Solving for x We can solve this system of equations by dividing the second equation by the first equation:
x p ( x + 10 ) p = 42.56 72.96
Simplifying, we get:
x x + 10 = 42.56 72.96
1 + x 10 = 42.56 72.96
x 10 = 42.56 72.96 − 1
x 10 = 42.56 72.96 − 42.56
x 10 = 42.56 30.4
Calculating the Tank Size Now, we can solve for x :
x = 30.4 10 × 42.56
x = 30.4 425.6
x = 14
Final Answer Therefore, the current size of Mrs. Hrang's tank is 14 gallons.
Examples
Understanding how tank size and fuel costs relate can help in various real-life scenarios. For instance, if you're planning a long road trip, knowing your car's tank size and fuel efficiency can help you estimate fuel costs. Similarly, if you're considering upgrading to a vehicle with a larger tank, you can calculate the potential increase in fuel expenses. This kind of math is also useful for businesses managing fleets of vehicles, helping them optimize fuel budgets and plan routes efficiently. By understanding these relationships, you can make informed decisions about vehicle maintenance, upgrades, and travel planning, ultimately saving money and time.
Mrs. Hrang's current gas tank size is 14 gallons based on the calculations established through the cost of filling the tank before and after the expansion. By determining the price per gallon and relating it to the tank sizes, we found the present size. Thus, the correct answer is 14 gallons.
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