The Mysteries of the Full Water Tank: Solving a Simple Math Problem

Have you ever encountered a math problem that seemed to be about water tanks, but left you scratching your head? This article will walk you through a practical real-life scenario involving a water tank and how to solve the puzzle surrounding its capacity. We will delve into the problem, provide a detailed solution, and explain every step to ensure a clear understanding.

Understanding the Problem

Imagine you have a water tank that is currently full of water, but after drawing 70 liters of water, it became full again. This unusual situation piques our interest in determining the tank's full capacity. Let's break down the problem and solve it step by step.

Formulating the Equation

First, let's denote the capacity of the tank as x liters. We can create an equation based on the conditions provided:

3/4x - 2400 1/5x

This equation reflects that initially, 75% of the tank was filled, and then 2400 liters were removed, leaving 20% of the tank filled.

Solving the Equation

To solve this equation, let's gather the x terms on the left and the pure numbers on the right:

3/4x - 1/5x 2400

Let's convert the fractions to have a common denominator:

15/2 - 4/2 2400

Simplifying the left side, we get:

11/2 2400

Now, solve for x by multiplying both sides by 20/11:

x 2400 * (20/11) ≈ 4363.64

Therefore, the full capacity of the tank is approximately 4363.64 liters.

Calculating the 3/9th of the Tank

To find out how much water the tank holds when it is 3/9 (or 1/3) full, we can simply take 1/3 of the full capacity:

1/3 * 4363.64 ≈ 1454.54 liters

Hence, when the tank is 1/3 full, it holds approximately 1454.54 liters.

Conclusion

Understanding how to solve such a problem involves breaking it down into simple, manageable steps, converting fractions to have a common denominator, and then solving for the unknown variable. This approach can be applied to various real-life scenarios involving liquid volumes and capacities.

Key Takeaways

Use a consistent system of measurement (either fractions or decimals) to avoid errors. 3/4 and 1/5 can be extrapolated to 15/20 and 4/20 for easier subtraction. 3/9 simplifies to 1/3, which can be used to calculate the 1/3 capacity of the tank.

Related Keywords

water tank capacity, math problem, full tank calculation