Math Problem Statement

Container A has 18.6 L of water. Container B has 10 300 ml of water. After an equal amount of water was removed from each container, container A now has 5 times as much water as container B. How many liters of water was removed from each container?

Solution

Let's denote the amount of water removed from each container as xx (in liters).

  • Initially, Container A has 18.6 L of water, and after removing xx liters, it will have 18.6x18.6 - x liters.
  • Container B has 10,300 mL of water, which is equivalent to 10.310.3 liters. After removing xx liters, it will have 10.3x10.3 - x liters.

According to the problem, after the water was removed, the amount of water in Container A is 5 times the amount of water in Container B. This gives us the equation:

18.6x=5×(10.3x)18.6 - x = 5 \times (10.3 - x)

Now, let's solve this equation.

18.6x=5(10.3x)18.6 - x = 5(10.3 - x) 18.6x=51.55x18.6 - x = 51.5 - 5x

Next, move the terms with xx to one side and the constants to the other side:

5xx=51.518.65x - x = 51.5 - 18.6 4x=32.94x = 32.9

Now, solve for xx:

x=32.94=8.225litersx = \frac{32.9}{4} = 8.225 \, \text{liters}

Thus, 8.225 liters of water were removed from each container.

Final Answer:

8.225 liters of water were removed from each container.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How would the answer change if Container A had more initial water?
  2. What happens if no water is removed from one of the containers?
  3. Can you express the relationship between the final volumes of water in a general form?
  4. What if Container B originally had 12,000 mL of water instead of 10,300 mL?
  5. How would this problem change if Container B was emptied after removing the water?

Tip: Always convert units (like milliliters to liters) before solving, to avoid confusion with mixed units.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Unit Conversion

Formulas

A - x = 5 * (B - x)
Unit conversion: 1 L = 1000 mL

Theorems

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Suitable Grade Level

Grades 6-8