Math Problem Statement

containers A and B had an equal amount of water at first. After 25.5 L of water from container A and 44.5 L of water from container B were used, container A had 5 times as much water as container B. how much water was in container b at first

Solution

Let's define the initial amount of water in containers AA and BB as xx liters each. Since both containers had the same initial amount of water, we know:

  • Amount of water in container AA after usage: x25.5x - 25.5 liters.
  • Amount of water in container BB after usage: x44.5x - 44.5 liters.

After using some water, container AA has 5 times as much water as container BB. This gives us the equation:

x25.5=5(x44.5)x - 25.5 = 5(x - 44.5)

Let's solve this equation step-by-step:

  1. Expand the equation:

x25.5=5x222.5x - 25.5 = 5x - 222.5

  1. Rearrange to isolate xx on one side:

x5x=222.5+25.5x - 5x = -222.5 + 25.5

4x=197-4x = -197

  1. Divide by -4:

x=1974x = \frac{-197}{-4}

x=49.25x = 49.25

Therefore, the initial amount of water in container BB was 49.25 liters.

Would you like more details or have any questions?

Here are 5 related questions to consider:

  1. What if the water usage amounts were different for containers A and B?
  2. How would the problem change if container A had twice the initial amount of water as container B?
  3. Can you solve similar problems with more than two containers?
  4. What if we only knew the ratio of the remaining water instead of the actual amounts?
  5. How would this problem change if water was added instead of removed?

Tip: Always double-check the logic in word problems by translating them into clear equations step-by-step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Equation: x - 25.5 = 5(x - 44.5)

Theorems

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Suitable Grade Level

Grades 6-8