Final answer:
To determine the remaining gas in Mr. Schmidt's car, calculate 1/4 of the tank's capacity, which is 3.8 gallons.
Step-by-step explanation:
To solve this problem, we need to find out how much gas is left in Mr. Schmidt's car when the gauge shows that 1/4 of the tank is remaining.
Mr. Schmidt's car has a gas tank that holds 15 1/5 gallons. First, we convert 15 1/5 gallons into an improper fraction to make the calculation easier.
Since 1/5 is the same as 3/15, to combine this with 15 (which is the same as 75/5), we get:
15 gallons + 3/15 gallons = 75/5 + 3/15
We now need to find a common denominator, which is 15:
= (75 × 3)/(5 × 3) + 3/15
= 225/15 + 3/15
= 228/15 gallons
So the total capacity of the gas tank in gallons is 228/15.
Now, we're told that the gauge shows 1/4 of a tank remaining, which means that we need to find out what 1/4 of 228/15 gallons is. To calculate this, we multiply the total capacity by the fraction that represents the remaining gas:
Gallons remaining = Total gas tank capacity × percentage remaining
= (228/15) × (1/4)
Now, multiplying these two fractions is straightforward:
= 228/15 × 1/4
We multiply numerators together and denominators together:
= 228 × 1 / 15 × 4
= 228 / 60
Both the numerator and the denominator can be divided by 12:
= 19 / 5
Since 19/5 is an improper fraction, we can convert it back to a mixed number to make it easier to understand in the context of gallons. 19 divided by 5 is 3 with a remainder of 4:
= 3 4/5 gallons
This means that, when the gas gauge shows 1/4 of a tank remaining in Mr. Schmidt's car, there are 3 4/5 gallons left in the tank. Converting 4/5 of a gallon to decimal, we have:
4/5 = 0.8
Therefore, 3 4/5 gallons equals 3.8 gallons. Hence, there are 3.8 gallons of gas remaining in the tank.