You surveyed 12,000 people and 1/4 responded by indicating a 5 to 1 preference

To interpret this survey:

1. **Total respondents**: 12,000 people were surveyed.
2. **Respondents with a preference**: 1/4 of them responded with a 5 to 1 preference. This means \( \frac{1}{4} \) of 12,000 people, or:
   \[
   \frac{12,000}{4} = 3,000
   \]
   people indicated a preference.

3. **The 5 to 1 preference**: Out of these 3,000 respondents, the 5 to 1 ratio means for every 6 people who expressed a preference, 5 prefer one option (let’s call it Option A) and 1 prefers the other (Option B).

4. **Breakdown of preference**:
   \[
   \frac{5}{6} \times 3,000 = 2,500 \text{ people prefer Option A}
   \]
   \[
   \frac{1}{6} \times 3,000 = 500 \text{ people prefer Option B}
   \]

So, from the 3,000 respondents:
- 2,500 people prefer Option A.
- 500 people prefer Option B.

Would you like more details or explanations?

Here are 5 related questions to think about:
1. What percentage of the total surveyed people prefer Option A?
2. What percentage of the total surveyed people prefer Option B?
3. How many people in total did not respond with a preference?
4. What would happen if the preference ratio were 4 to 2 instead of 5 to 1?
5. If the survey were expanded to 20,000 people, how many would you expect to prefer Option A?

**Tip**: Ratios are useful for distributing quantities based on proportional relationships.

You surveyed 12,000 people and 1/4 responded by indicating a 5 to 1 preference.

Explore how to analyze a survey of 12,000 people where 1/4 responded with a 5 to 1 preference ratio. Understand ratios and proportions with a detailed breakdown of 2,500 people preferring Option A and 500 preferring Option B. Suitable for Grades 6-8.

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