the gasoline gauge on a van read 1/4 full when 10 gallons were added to the tank, the gauge read 2/3 full how many more gallons are needed to fill the tank?
x/4 + 10 = 2x/3
x = 24
6+10=16
still need 8 gallons
where does 6 + 10 = 18 come from ?
To find out how many more gallons are needed to fill the tank, we need to determine the capacity of the tank first.
Assuming the tank is fully filled when the gauge reads 2/3, we can calculate the fraction of the tank filled with 10 gallons.
Let's work through the steps:
1. Start with the initial fraction read by the gauge, which is 1/4.
2. Since 10 gallons were added to the tank, the fraction filled by these 10 gallons is also 1/4 (since the gauge read 1/4 full initially).
3. After adding the 10 gallons, the gauge then reads 2/3 full. So, the fraction represented by these 10 gallons is 2/3 - 1/4.
4. To determine the capacity of the tank, we need to find the difference between a full tank (when the gauge reads 2/3) and the fraction represented by the additional 10 gallons.
(2/3) - (2/3 - 1/4)
= (2/3) - (8/12 - 3/12)
= (2/3) - (5/12)
= (8/12) - (5/12)
= 3/12
= 1/4
5. Since the 10 gallons filled the tank up to 1/4 of its capacity, we need to determine how much more is required to reach a full tank, which is 1 - 1/4.
= 3/4
6. To find out how much gasoline is needed to fill the tank completely, we need to calculate it as a fraction of the tank's capacity.
= (3/4) * (tank capacity)
Let's assume the tank capacity is x gallons.
= (3/4) * x
7. Therefore, the number of more gallons needed to fill the tank completely is (3/4) * x.