The Gas Tank Of Dave's Car Has A Capacity Of 12 Gallons. The Tank Was 3 8 \frac{3}{8} 8 3 ​ Full Before Dave Filled It To Capacity. It Cost Him $ 2.50 \$ 2.50 $2.50 Per Gallon Of Gas. How Much Did Dave Spend, In Dollars, To Fill The Tank To Capacity?A.

Introduction

In this problem, we are given the capacity of Dave's car gas tank, which is 12 gallons. The tank was initially $\frac{3}{8}$ full, and Dave filled it to capacity. We need to find out how much he spent, in dollars, to fill the tank to capacity. To solve this problem, we will use mathematical concepts and formulas.

Understanding the Problem

Let's break down the problem and understand what is given and what is required.

• The gas tank has a capacity of 12 gallons.
• The tank was initially $\frac{3}{8}$ full.
• The cost of gas is $\$ 2.50$ per gallon.
• We need to find out how much Dave spent to fill the tank to capacity.

Calculating the Initial Amount of Gas

To find out how much gas was initially in the tank, we need to multiply the capacity of the tank by the fraction that was full.

Initial\ amount\ of\ gas = Capacity \times Fraction\ full
Initial\ amount\ of\ gas = 12 \times \frac{3}{8}
Initial\ amount\ of\ gas = 12 \times 0.375
Initial\ amount\ of\ gas = 4.5\ gallons

Calculating the Amount of Gas Needed to Fill the Tank

To find out how much gas is needed to fill the tank to capacity, we need to subtract the initial amount of gas from the capacity of the tank.

Amount\ of\ gas\ needed = Capacity - Initial\ amount\ of\ gas
Amount\ of\ gas\ needed = 12 - 4.5
Amount\ of\ gas\ needed = 7.5\ gallons

Calculating the Total Cost

To find out how much Dave spent to fill the tank to capacity, we need to multiply the amount of gas needed by the cost of gas per gallon.

Total\ cost = Amount\ of\ gas\ needed \times Cost\ per\ gallon
Total\ cost = 7.5 \times 2.50
Total\ cost = 18.75

Conclusion

In this problem, we used mathematical concepts and formulas to find out how much Dave spent to fill the tank to capacity. We calculated the initial amount of gas, the amount of gas needed to fill the tank, and the total cost. The total cost is $\$ 18.75$.

Final Answer

Q&A: Frequently Asked Questions

Q: What is the capacity of Dave's car gas tank? A: The capacity of Dave's car gas tank is 12 gallons.

Q: How much gas was initially in the tank? A: To find out how much gas was initially in the tank, we need to multiply the capacity of the tank by the fraction that was full. The initial amount of gas is 4.5 gallons.

Q: How much gas is needed to fill the tank to capacity? A: To find out how much gas is needed to fill the tank to capacity, we need to subtract the initial amount of gas from the capacity of the tank. The amount of gas needed is 7.5 gallons.

Q: How much did Dave spend to fill the tank to capacity? A: To find out how much Dave spent to fill the tank to capacity, we need to multiply the amount of gas needed by the cost of gas per gallon. The total cost is $\$ 18.75$.

Q: What is the cost of gas per gallon? A: The cost of gas per gallon is $\$ 2.50$.

Q: What is the fraction that the tank was initially full? A: The fraction that the tank was initially full is $\frac{3}{8}$.

Q: How do I calculate the initial amount of gas? A: To calculate the initial amount of gas, you need to multiply the capacity of the tank by the fraction that was full. The formula is: Initial amount of gas = Capacity × Fraction full.

Q: How do I calculate the amount of gas needed to fill the tank? A: To calculate the amount of gas needed to fill the tank, you need to subtract the initial amount of gas from the capacity of the tank. The formula is: Amount of gas needed = Capacity - Initial amount of gas.

Q: How do I calculate the total cost? A: To calculate the total cost, you need to multiply the amount of gas needed by the cost of gas per gallon. The formula is: Total cost = Amount of gas needed × Cost per gallon.

Conclusion

In this Q&A article, we answered some frequently asked questions related to the gas tank filling problem. We provided step-by-step solutions to calculate the initial amount of gas, the amount of gas needed to fill the tank, and the total cost. We also provided formulas to help you calculate these values.

Final Answer

The final answer is $\boxed{18.75}$.