Answer: [tex]24\ liters[/tex]
Step-by-step explanation:
Let be "x" the amount of gasoline in liters that the car's tank had at the beginning of the trip.
1. In the first part of the trip the amount of gasoline the car used can be expressed as:
[tex]\frac{2}{3}x[/tex]
2. After the first part of the trip, the remaining was:
[tex]x-\frac{2}{3}x=\frac{1}{3}x[/tex]
3. In the second part of the trip the car used [tex]\frac{1}{2}[/tex] of the remaining. This is:
[tex](\frac{1}{3}x)(\frac{1}{2})=\frac{1}{6}x[/tex]
4. The total amount ot gasoline used in this trip was 20 liters.
5. Then, with this information, you can write the following equation:
[tex]\frac{2}{3}x+\frac{1}{6}x=20[/tex]
6. Finally, you must solve for "x" in order to find its value. This is:
[tex]\frac{2}{3}x+\frac{1}{6}x=20\\\\\frac{5}{6}x=20\\\\5x=120\\\\x=24[/tex]
