To solve this problem step-by-step, follow these steps:

Problem Analysis

You are given:

1. A total of 30 people at the party.
2. People could either choose a hamburger or a pizza.
3. There are 5 times as many hamburgers as pizzas.

You need to find the number of people who chose hamburgers and pizzas.

Steps to Solve:

1. Assign variables: Let the number of people who chose pizzas = $x$. Then, the number of people who chose hamburgers = $5x$ (because it is 5 times as many as pizzas).

2. Form an equation: Since the total number of people is 30, we can write: $x + 5x = 30$

3. Simplify the equation: Combine like terms: $6x = 30$

4. Solve for $x$: Divide both sides by 6: $x = 5$

5. Interpret the result:

   • $x = 5$: Number of pizzas.
   • $5x = 5 \times 5 = 25$: Number of hamburgers.

Final Answer:

• Number of pizzas: 5
• Number of hamburgers: 25

Would you like further clarification or additional examples?

Related Questions:

1. What if the ratio was 3 times instead of 5 times as many hamburgers as pizzas?
2. How would the result change if the total number of people was 50?
3. Can you explain why $x$ represents pizzas and not hamburgers?
4. What if the ratio was reversed (5 times more pizzas than hamburgers)?
5. How would you set up the problem if there were an unknown number of total attendees?

Tip:

Always define your variables clearly and double-check your calculations when dealing with ratios or proportions.