Question

6. A catering company is setting up for a wedding. They expect 150 people toattend. They can provide small tables that seat 6 people and large tables thatseat 10 people.6a. Find a combination of small and large tables that seats exactly 150people. *Your answer6b. Let x represent the number of small tables and y represent the numberof large tables. Write an equation to represent the relationship between xand y.

Answer 1

6a.

Since each small table seats 6 people and large tables seat 10 people, a possible combination for 150 people would be 10 small tables and 9 large tables

(10 * 6 + 9 * 10 = 60 + 90 = 150)

6b.

The relationship between x and y is given by the following equation:

$6x+10y=150$

This relationship represents the number of people of each type of table being added to the total number of people.

6c.

The point (20, 5) means that we would have x = 20 and y = 5, that is, 20 small tables and 5 large tables.

6d.

Let's use this point in the equation and check if the result is true:

$\begin{gathered} 6x+10y=150 \\ 6\cdot20+10\cdot5=150 \\ 120+50=150 \\ 170=150\text{ (false)} \end{gathered}$

Since the result is not true, the point (20, 5) is not a solution to the equation.