Given the problem, let's solve for the number of square tables, [tex]\( x \)[/tex], when [tex]\( y = 9 \)[/tex].
1. Understand the variables:
- [tex]\( x \)[/tex]: Number of square tables.
- [tex]\( y \)[/tex]: Number of round tables, given as [tex]\( y = 9 \)[/tex].
- Each square table can fit 8 people.
- Each round table can fit 6 people.
- The total number of people to be accommodated is 150.
2. Calculate the number of people accommodated by the round tables:
Since [tex]\( y = 9 \)[/tex] and each round table can fit 6 people:
[tex]\[
\text{People by round tables} = 9 \times 6 = 54
\][/tex]
3. Determine the remaining number of people to be accommodated by square tables:
Total number of people is 150. After seating 54 people at the round tables:
[tex]\[
\text{Remaining people} = 150 - 54 = 96
\][/tex]
4. Calculate the number of square tables needed to accommodate the remaining people:
Each square table accommodates 8 people:
[tex]\[
x = \frac{\text{Remaining people}}{\text{People per square table}} = \frac{96}{8} = 12
\][/tex]
Therefore, the committee needs [tex]\( 12 \)[/tex] square tables to accommodate the remaining people.
So, the complete solution is:
- The variable [tex]\( y \)[/tex] represents the number of round tables.
- If [tex]\( y = 9 \)[/tex], the value of [tex]\( x \)[/tex] is 12.
- The committee needs [tex]\( 12 \)[/tex] square tables.
