A water tank is 2/3 full.when 3000 liters are drawn from the tank, it becomes 1/4 full.How many liters can it hold when 5/6 full?
2/3 x - 3000 = 1/4 x
Solve for x, and then find 5/6 x
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Let's solve this problem step-by-step:
Step 1: Determine the initial capacity of the water tank
Let's assume the initial capacity of the water tank to be x liters.
Step 2: Determine the amount of water initially in the tank
According to the problem, the water tank is initially 2/3 full. Therefore, the amount of water initially in the tank is given by (2/3) * x.
Step 3: Determine the new capacity of the water tank after 3000 liters are drawn
When 3000 liters are drawn from the tank, it becomes 1/4 full. Therefore, the new capacity of the water tank is (1/4) * x.
Step 4: Determine the new amount of water in the tank after 3000 liters are drawn
According to the problem, the amount of water in the tank after 3000 liters are drawn is given by (1/4) * x.
Step 5: Calculate the difference in the amount of water before and after 3000 liters are drawn
The difference in the amount of water before and after 3000 liters are drawn is given by (2/3) * x - (1/4) * x.
Step 6: Set up an equation to find the value of x
We can set up the equation as follows:
(2/3) * x - (1/4) * x = 3000
Step 7: Solve the equation for x
To solve the equation, we can simplify it by finding a common denominator and combining like terms:
(8/12) * x - (3/12) * x = 3000
(5/12) * x = 3000
Solving for x, we get:
x = (3000 * 12) / 5
x = 7200
Step 8: Calculate the capacity of the water tank when it is 5/6 full
To find the capacity of the water tank when it is 5/6 full, we can multiply the initial capacity (x) by 5/6:
Capacity = (7200 * 5) / 6
Capacity = 6000
Therefore, the water tank can hold 6000 liters when it is 5/6 full.
To solve this problem, we can break it down into steps:
Step 1: Determine the current capacity of the water tank
Let's assume the capacity of the tank is V liters.
Given that the tank is 2/3 full when 3000 liters are drawn from it, we can set up the following equation:
(2/3) * V - 3000 = 1/4 * V
Step 2: Solve the equation to find the total capacity
To solve the equation, we need to simplify it by getting rid of the fractions.
Multiply the equation through by the least common denominator (LCD) of 3 and 4, which is 12:
12 * [(2/3) * V - 3000] = 12 * (1/4 * V)
After simplifying, we get:
8V - 36000 = 3V
Combine like terms:
8V - 3V = 36000
Simplify the equation:
5V = 36000
Divide both sides by 5:
V = 36000 / 5
Therefore, the original capacity of the water tank is 7200 liters.
Step 3: Calculate the capacity when 5/6 full
To find out how many liters the tank can hold when it's 5/6 full, we can simply multiply the total capacity by 5/6.
(5/6) * 7200 = 6000
Therefore, the tank can hold 6000 liters of water when it's 5/6 full.