Math Problem Statement
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 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:
-
Before mixing:
- Container A: 400 mL milk, 0 mL coffee.
- Container B: mL of coffee.
-
After transferring 200 mL of coffee from B to A:
- Container A: 400 mL of milk, 200 mL of coffee.
- Container B: mL of coffee.
-
Final condition (ratio of coffee):
- The amount of coffee in A to the remaining coffee in B is 5:2. This gives the equation:
-
Solving the equation:
- Cross-multiply:
- Solve for :
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:
- What would happen if you transferred 300 mL of coffee instead of 200 mL?
- How would the ratio change if container A initially had 500 mL of milk?
- What if the final ratio was 3:1 instead of 5:2?
- How much coffee would need to be transferred to make the ratio 4:3?
- 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
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