Math Problem Statement

A container A has 400 mL of milk. Container B has an unknown amount of coffee. 200 mL of coffee is transferred from container B to container A. After this transfer, the ratio of coffee in container A to the remaining coffee in container B becomes 5:2. How much coffee was originally in container B?

Solution

The problem in the image is written in Japanese and can be summarized as follows:

  • Container A has 400 mL of milk.
  • Container B has an unknown amount of coffee (let’s call it xx mL).
  • 200 mL of coffee is taken from container B and added to container A.
  • After this, the ratio of the amount of coffee in container A to the amount of coffee remaining in container B becomes 5:2.

The question is asking: How much coffee was originally in container B?

Steps to solve:

  1. Before mixing:

    • Container A: 400 mL milk, 0 mL coffee.
    • Container B: xx mL of coffee.
  2. After transferring 200 mL of coffee from B to A:

    • Container A: 400 mL of milk, 200 mL of coffee.
    • Container B: x200x - 200 mL of coffee.
  3. Final condition (ratio of coffee):

    • The amount of coffee in A to the remaining coffee in B is 5:2. This gives the equation: 200x200=52\frac{200}{x - 200} = \frac{5}{2}
  4. Solving the equation:

    • Cross-multiply: 200×2=5×(x200)200 \times 2 = 5 \times (x - 200) 400=5x1000400 = 5x - 1000
    • Solve for xx: 5x=14005x = 1400 x=280x = 280

Thus, the original amount of coffee in container B was 280 mL.

Would you like further clarification on any steps?

Here are 5 related questions for further practice:

  1. What would happen if you transferred 300 mL of coffee instead of 200 mL?
  2. How would the ratio change if container A initially had 500 mL of milk?
  3. What if the final ratio was 3:1 instead of 5:2?
  4. How much coffee would need to be transferred to make the ratio 4:3?
  5. What is the final amount of liquid in container A after the transfer?

Tip: Always check the units when dealing with mixture problems, to ensure consistency across all quantities.

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Math Problem Analysis

Mathematical Concepts

Ratios
Basic Algebra
Mixture Problems

Formulas

Ratio Formula: A/B = a/b
Basic Algebra: Solving linear equations

Theorems

Proportional Reasoning

Suitable Grade Level

Grades 6-8