When 6 gallons of gasoline are put into a car's tank the indicator goes from 1/4 of a tank to 5/8. What is the total capacity of the gas tank?
let the number of gallons in the tank be x
(5/8)x - (1/4)x = 6
(3/8)x=6
x = 16
check:
1/4 full would be 4 gall
5/8 full would be 10 gallons
must have put in 6 gallons, all is good!
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Initially the tank had 1/4 of gasoline. Then 6 gallons is added and the tank now has 5/8
Write the expression like this
1/4 + 6 litres = 5/8
Then subtract 1/4 from both sides to isolate 6 litres
1/4-1/4 + 6litres= 5/8-1/4
6 litres = 5/8-1/4
6litres = 3/8
So 3/8 of full tank is 6 litres
What is the full tank?
Let the full tank be X litres
3/8 of X = 6 litres
So X = 6litres × 8/3
X = 16 litres
Well, let's see here. If 6 gallons of gasoline takes the indicator from 1/4 to 5/8, that means it goes up by 3/8. So, if we assume that the total capacity of the gas tank is x gallons, we can set up the equation:
6 gallons = (5/8 - 1/4) * x
Now, let's do some math and figure out the total capacity of the gas tank!
(5/8 - 1/4) * x = 6 gallons
(5/8 - 2/8) * x = 6 gallons
(3/8) * x = 6 gallons
x = (6 gallons) / (3/8)
x = (6 gallons) * (8/3)
x = 48/3
x = 16 gallons
So, the total capacity of the gas tank is 16 gallons! Now you have plenty of room for more fuel and more fun road trips. Just remember to make pit stops for snacks and dad jokes!
To find the total capacity of the gas tank, we need to determine the amount that corresponds to a full tank when the indicator is at 1.
In this case, a 6-gallon increase in gasoline caused the indicator to move from 1/4 to 5/8.
The difference between 5/8 and 1/4 is 5/8 - 1/4 = 5/8 - 2/8 = 3/8.
Since a 6-gallon increase corresponds to 3/8 of a tank, we can calculate the capacity of the gas tank using the proportion:
6 gallons = 3/8 tank capacity.
To find the capacity of a full tank, we can set up the following equation and solve for the unknown:
6 gallons * (8/3) = tank capacity.
Dividing 6 gallons by 3/8 is the same as multiplying it by 8/3.
The result is:
48/3 = tank capacity.
Simplifying, we get:
16 = tank capacity.
Therefore, the total capacity of the gas tank is 16 gallons.
To find the total capacity of the gas tank, we can use a proportion based on the information provided.
Let's assume that the total capacity of the gas tank is represented by 'x' gallons.
According to the given information, when 6 gallons of gasoline are added to the tank, the indicator goes from 1/4 to 5/8 of the tank.
This can be represented as:
6 / x = 5/8 - 1/4
To simplify this equation, we need to find a common denominator. The common denominator here is 8 because both fractions have a denominator of 8.
So, the equation becomes:
6 / x = 5/8 - 2/8
Now, we can subtract the numerators:
6 / x = 3/8
To isolate 'x', we can cross-multiply:
(6 * 8) = (3 * x)
48 = 3x
Dividing both sides of the equation by 3:
48 / 3 = x
x = 16
Therefore, the total capacity of the gas tank is 16 gallons.