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The problem describes the transfer of liquids between a glass and a cup, with milk and water being mixed. Let's break it down:

1. **Initial conditions**:
   - A glass contains 500 cc of milk.
   - A cup contains 500 cc of water.

2. **First transfer**:
   - 150 cc of milk is taken from the glass and added to the cup, which mixes thoroughly with the 500 cc of water in the cup.

3. **Second transfer**:
   - From the cup (which now contains a milk-water mixture), 150 cc of this mixture is transferred back to the glass.

We need to find the ratio of water in the glass to milk in the cup after these transfers.

### Step-by-step solution:

#### After first transfer (from glass to cup):
- The cup now has \( 500 \, \text{cc of water} + 150 \, \text{cc of milk} \) = 650 cc of a mixture.
- The glass is left with \( 500 \, \text{cc of milk} - 150 \, \text{cc of milk} = 350 \, \text{cc of milk} \).

#### After second transfer (from cup to glass):
- The 150 cc mixture taken from the cup has both water and milk in proportion to their amounts in the cup.
- The cup contains 500 cc of water and 150 cc of milk. The ratio of water to milk is \( \frac{500}{150} = \frac{10}{3} \).
- From the 150 cc of mixture transferred back to the glass, we can calculate:
  - Water in the mixture: \( \frac{10}{13} \times 150 = \frac{1500}{13} \approx 115.38 \, \text{cc} \)
  - Milk in the mixture: \( \frac{3}{13} \times 150 = \frac{450}{13} \approx 34.62 \, \text{cc} \)

#### Final state:
- The glass now contains \( 350 \, \text{cc of milk} + 115.38 \, \text{cc of water} \).
- The cup contains \( 500 - 115.38 = 384.62 \, \text{cc of water} \) and \( 150 - 34.62 = 115.38 \, \text{cc of milk} \).

Thus, the ratio of water in the glass to milk in the cup is:
\[
\frac{\text{Water in the glass}}{\text{Milk in the cup}} = \frac{115.38}{115.38} = 1:1
\]

### Answer: **Option 1: 1:1**

Would you like further details on any of these steps, or do you have any questions? 

Here are 5 related questions to deepen understanding:
1. What would the ratio be if 200 cc of milk was transferred instead of 150 cc?
2. How would the result change if the initial amounts of milk and water were different?
3. What is the impact of transferring a larger amount of the mixture back to the glass?
4. How would the concentration of milk in the cup change after multiple transfers?
5. What is the total volume of the mixture in both vessels after all transfers?

**Tip:** For problems involving mixtures and ratios, always calculate the proportions of each substance carefully before and after transfers to maintain accuracy.

A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

Determine the ratio of water in the glass to milk in the cup after transferring liquids between a glass and a cup. The problem involves concepts of ratios and mixtures, making it suitable for students in Grades 8-10.

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