Formulate but do not solve the problem.

In a survey of 1000 adults aged 18 and older, the following question was posed: "Are other travelers' online reviews trustworthy?" The participants were asked to answer "yes," "no," or "not sure." The survey revealed that 330 answered "no" or "not sure." It also showed that the number of those who answered "yes" exceeded the number of those who answered "no" by 420. What percentage of respondents answered "yes," "no," and "not sure"? (Let x represent the number of respondents who answered "yes", y represent the number of respondents who answered "no", and z represent the number of respondents who answered "not sure".)

We can formulate the problem using three variables:
- Let \( x \) represent the number of respondents who answered "yes."
- Let \( y \) represent the number of respondents who answered "no."
- Let \( z \) represent the number of respondents who answered "not sure."

From the problem, we can derive the following conditions:

1. The total number of respondents is 1000, so the sum of all responses must equal 1000:
   \[
   x + y + z = 1000
   \]
   
2. The number of respondents who answered "no" or "not sure" is given as 330:
   \[
   y + z = 330
   \]
   
3. The number of respondents who answered "yes" exceeds the number of those who answered "no" by 420:
   \[
   x = y + 420
   \]

Using these three conditions, you can solve for \( x \), \( y \), and \( z \) to determine the number of respondents who answered "yes," "no," and "not sure." Once the values are found, you can calculate the percentage of respondents for each category by dividing each number by 1000 and multiplying by 100.

Would you like to proceed with solving this system of equations?

### Expanding your understanding:
1. How would you describe the relationship between "yes" and "no" respondents?
2. Why does knowing the total of "no" and "not sure" responses help simplify the problem?
3. Can we rewrite the first equation using the other two to express it in terms of just one variable?
4. How do you calculate percentages once you know the individual values of \(x\), \(y\), and \(z\)?
5. What role does the total number of respondents (1000) play in determining the percentage?

**Tip**: When faced with multiple unknowns, try to express as many variables as possible in terms of one variable to simplify your calculations.

In a survey of 1000 adults aged 18 and older, the following question was posed: 'Are other travelers' online reviews trustworthy?' The participants were asked to answer 'yes,' 'no,' or 'not sure.' The survey revealed that 330 answered 'no' or 'not sure.' It also showed that the number of those who answered 'yes' exceeded the number of those who answered 'no' by 420. What percentage of respondents answered 'yes,' 'no,' and 'not sure'? (Let x represent the number of respondents who answered 'yes', y represent the number of respondents who answered 'no', and z represent the number of respondents who answered 'not sure'.)

Solve a system of equations based on a survey of 1000 respondents answering 'yes,' 'no,' or 'not sure' to a travel-related question. Learn how to calculate the percentage of each response using algebraic methods. Suitable for students in Grades 8-10.

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