A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people.

a. Find a combination of small and large tables that seats exactly 150 people.

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10 small tables and 9 large tables

b. Let
represent the number of small tables and
represent the number of large tables. Write an equation to represent the relationship between
and
.

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c. Explain what the point (20,5)
means in this situation.

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d. Is the point
a solution to the equation you wrote?

Select the correct choice.

A
Yes
B
No
Explain your reasoning.

Type your response in the space below.

Let's address each part of the problem:

### Part a:
You are given the combination of 10 small tables and 9 large tables, which together seat exactly 150 people. This is correct because:

- 10 small tables seat \(10 \times 6 = 60\) people.
- 9 large tables seat \(9 \times 10 = 90\) people.

Together, they seat \(60 + 90 = 150\) people.

### Part b:
Let:
- \(x\) represent the number of small tables.
- \(y\) represent the number of large tables.

Each small table seats 6 people, and each large table seats 10 people. So, the equation representing the total number of seats for 150 people is:

\[
6x + 10y = 150
\]

### Part c:
The point \((20, 5)\) represents 20 small tables and 5 large tables. Substituting \(x = 20\) and \(y = 5\) into the equation:

- \(20\) small tables seat \(20 \times 6 = 120\) people.
- \(5\) large tables seat \(5 \times 10 = 50\) people.

Together, they seat \(120 + 50 = 170\) people. So, the

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people. a. Find a combination of small and large tables that seats exactly 150 people. b. Let x represent the number of small tables and y represent the number of large tables. Write an equation to represent the relationship between x and y. c. Explain what the point (20,5) means in this situation. d. Is the point (20,5) a solution to the equation you wrote? Select the correct choice. A. Yes B. No. Explain your reasoning.

This problem helps you find the right combination of small and large tables to seat 150 guests at a wedding. Using a linear equation 6x + 10y = 150, learn how to solve the problem and analyze specific points like (20,5). Ideal for students in Grades 6-8.

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