Gasoline fuel

You just drove your car 300 miles and used 40 gallons of gas. You know that the gas tank on your car holds 12 1/2 gallons of gas; if the gas you buy is $2.50 per gallon. What would you pay to fill one-half of your tank?

Correct answer:

x =  15.625 USD

Step-by-step explanation:

$$\begin{gathered} V_1=12{\displaystyle \frac{1}{2}}=12+{\displaystyle \frac{1}{2}}={\displaystyle \frac{12\cdot 2+1}{2}}={\displaystyle \frac{25}{2}}=12.5\text{ gal } \\ {V}_2=V_1\mathrm{/}2=12.5\mathrm{/}2={\displaystyle \frac{25}{4}}=6.25\text{ gal } \\ x=2.5\cdot V_2=2.5\cdot 6.25={\displaystyle \frac{125}{8}}\text{ USD}=15\frac{5}{8}\text{ USD}=15.625\text{ USD} \end{gathered}$$

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