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Answer :
To solve the problem of determining the seating arrangement for Mackenzie's graduation party, we need to find the correct inequality that describes the situation using the provided table seating capacities and expected guests.
1. Identify Variables and Their Meanings:
- Let [tex]\( x \)[/tex] be the number of circular tables.
- Let [tex]\( y \)[/tex] be the number of rectangular tables.
2. Determine Seating Capacity:
- A circular table can seat 8 guests.
- A rectangular table can seat 9 guests.
3. Set Up the Inequality:
- The goal is to seat at least 197 guests.
- Therefore, the total number of guests that can be seated using the tables is represented by the expression [tex]\( 8x + 9y \)[/tex], where:
- [tex]\( 8x \)[/tex] is the number of guests seated at circular tables.
- [tex]\( 9y \)[/tex] is the number of guests seated at rectangular tables.
4. Define the Inequality:
- To meet the requirement of seating at least 197 guests, the expression should be greater than or equal to 197.
- This gives us the inequality:
[tex]\[
8x + 9y \geq 197
\][/tex]
5. Select the Correct Option:
- Among the options given, the inequality that matches our setup is [tex]\( 8x + 9y \geq 197 \)[/tex].
Thus, the correct inequality that describes the seating arrangement for Mackenzie’s graduation party is [tex]\( 8x + 9y \geq 197 \)[/tex].
1. Identify Variables and Their Meanings:
- Let [tex]\( x \)[/tex] be the number of circular tables.
- Let [tex]\( y \)[/tex] be the number of rectangular tables.
2. Determine Seating Capacity:
- A circular table can seat 8 guests.
- A rectangular table can seat 9 guests.
3. Set Up the Inequality:
- The goal is to seat at least 197 guests.
- Therefore, the total number of guests that can be seated using the tables is represented by the expression [tex]\( 8x + 9y \)[/tex], where:
- [tex]\( 8x \)[/tex] is the number of guests seated at circular tables.
- [tex]\( 9y \)[/tex] is the number of guests seated at rectangular tables.
4. Define the Inequality:
- To meet the requirement of seating at least 197 guests, the expression should be greater than or equal to 197.
- This gives us the inequality:
[tex]\[
8x + 9y \geq 197
\][/tex]
5. Select the Correct Option:
- Among the options given, the inequality that matches our setup is [tex]\( 8x + 9y \geq 197 \)[/tex].
Thus, the correct inequality that describes the seating arrangement for Mackenzie’s graduation party is [tex]\( 8x + 9y \geq 197 \)[/tex].
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