Question

1. 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? explain your reasoning.

Explanation:

Step1: Set up the equation

Let \(x\) be the number of small tables (seating \(6\) people each) and \(y\) be the number of large tables (seating \(10\) people each). The total number of people is \(150\). So the equation is \(6x + 10y=150\).

Step2: Check if \((20,5)\) is a solution

Substitute \(x = 20\) and \(y = 5\) into the equation \(6x+10y\).

$$
LATEXBLOCK0
$$

Since \(170
eq150\), \((20,5)\) is not a solution.

Step3: Explain the meaning of the equation

The equation \(6x + 10y=150\) represents the relationship between the number of small tables (\(x\)) and large tables (\(y\)) such that the total number of seats ( \(6x\) from small tables and \(10y\) from large tables) equals the expected number of people (\(150\)).

Answer:

a. The equation is \(6x + 10y=150\).
b. The equation \(6x + 10y = 150\) means that the sum of the number of seats from small tables (\(6x\)) and large tables (\(10y\)) is equal to the total number of expected guests (\(150\)).
c. The point \((20,5)\) means \(20\) small tables and \(5\) large tables. Substituting \(x = 20\) and \(y = 5\) into \(6x+10y\) gives \(6\times20+10\times5=120 + 50=170
eq150\), so \((20,5)\) is not a solution to the equation \(6x + 10y=150\).