Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank  2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?

Let's analyze the situation step by step for both Joe and JoAnn.

### Joe:
1. Joe starts with **12 ounces of coffee** in his 16-ounce cup.
2. He drinks **2 ounces** of his coffee, leaving him with **10 ounces of coffee** in the cup.
3. Joe then adds **2 ounces of cream**, so his cup now contains:
   - 10 ounces of coffee
   - 2 ounces of cream

The total liquid in Joe's cup is now **12 ounces** (10 ounces of coffee + 2 ounces of cream).

### JoAnn:
1. JoAnn starts with **12 ounces of coffee** in her 16-ounce cup.
2. She adds **2 ounces of cream**, so her cup now contains:
   - 12 ounces of coffee
   - 2 ounces of cream
   
   This gives her a total of **14 ounces of liquid** in the cup (12 ounces of coffee + 2 ounces of cream).
3. JoAnn stirs the mixture thoroughly, so the cream is distributed evenly throughout the 14-ounce mixture.
   - The proportion of cream in the mixture is \( \frac{2}{14} = \frac{1}{7} \).
4. JoAnn drinks **2 ounces** of the mixture, and since the cream is evenly distributed, the amount of cream in the 2 ounces she drinks is:
   \[
   2 \times \frac{1}{7} = \frac{2}{7} \text{ ounces of cream}
   \]
   - So after drinking, JoAnn has \( 14 - 2 = 12 \) ounces of liquid left, and the amount of cream left in her cup is:
   \[
   2 - \frac{2}{7} = \frac{14}{7} - \frac{2}{7} = \frac{12}{7} \text{ ounces of cream}
   \]
   - The remaining amount of coffee is \( 12 - \frac{12}{7} = \frac{84}{7} - \frac{12}{7} = \frac{72}{7} = 10 \frac{2}{7} \text{ ounces of coffee} \).

### Ratio of the amount of cream:
- Joe has **2 ounces of cream** in his coffee.
- JoAnn has **\( \frac{12}{7} \) ounces of cream**.

Thus, the ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee is:
\[
\frac{2}{\frac{12}{7}} = 2 \times \frac{7}{12} = \frac{14}{12} = \frac{7}{6}
\]

So, the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee is **7:6**.

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Do you have any questions, or would you like further details?

Here are 5 related questions to explore further:
1. What is the percentage of cream in Joe's coffee after the process?
2. What is the percentage of cream in JoAnn's coffee after she drinks?
3. If both drank 3 ounces instead of 2 ounces, how would the ratio change?
4. How would the problem change if JoAnn added 3 ounces of cream instead of 2 ounces?
5. What is the total amount of liquid in each person's cup after their actions?

**Tip:** Always ensure proportions are distributed properly when dealing with mixtures, especially after adding and removing portions.

Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?

Explore a step-by-step solution to find the ratio of cream in Joe's coffee to JoAnn's after a series of actions, involving drinking coffee and adding cream. Learn key concepts in ratios, proportions, and mixture problems. Suitable for Grades 9-12.

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