Question
In the cafeteria, there is one large table with 10 seats and many smaller tables with 4 seats. The cafeteria has a fire code restriction that the room can hold a maximum of 70 students. If a student is seated at every seat at each table, how many small tables can be in the cafeteria without breaking the fire code?
You're trying to figure out the inequality symbol. Start by substituting a value below the boundary, x=14, and a value above the boundary, x=16, in the inequality. Does each make the inequality true or false?
x=14 x=15 (boundary) x=16
10+4x≤70
True
You're trying to figure out the inequality symbol. Start by substituting a value below the boundary, x=14, and a value above the boundary, x=16, in the inequality. Does each make the inequality true or false?
x=14 x=15 (boundary) x=16
10+4x≤70
True
Answers
GPT-4o mini
To determine how many small tables can be in the cafeteria without breaking the fire code, we start with the inequality that represents the seating capacity:
\[ 10 + 4x \leq 70 \]
where \( x \) is the number of small tables.
Let's solve the inequality:
1. Subtract 10 from both sides:
\[ 4x \leq 60 \]
2. Divide by 4:
\[ x \leq 15 \]
This tells us that the maximum number of small tables \( x \) is 15.
Now, let's check the values you provided:
- For \( x = 14 \):
\[ 10 + 4(14) = 10 + 56 = 66 \]
Since \( 66 \leq 70 \), this is **True**.
- For \( x = 15 \) (the boundary):
\[ 10 + 4(15) = 10 + 60 = 70 \]
Since \( 70 \leq 70 \), this is also **True**.
- For \( x = 16 \):
\[ 10 + 4(16) = 10 + 64 = 74 \]
Since \( 74 \leq 70 \) is **False**, this indicates that having 16 small tables exceeds the fire code limit.
Therefore, the maximum number of small tables that can be in the cafeteria without violating the fire code is **15**.
\[ 10 + 4x \leq 70 \]
where \( x \) is the number of small tables.
Let's solve the inequality:
1. Subtract 10 from both sides:
\[ 4x \leq 60 \]
2. Divide by 4:
\[ x \leq 15 \]
This tells us that the maximum number of small tables \( x \) is 15.
Now, let's check the values you provided:
- For \( x = 14 \):
\[ 10 + 4(14) = 10 + 56 = 66 \]
Since \( 66 \leq 70 \), this is **True**.
- For \( x = 15 \) (the boundary):
\[ 10 + 4(15) = 10 + 60 = 70 \]
Since \( 70 \leq 70 \), this is also **True**.
- For \( x = 16 \):
\[ 10 + 4(16) = 10 + 64 = 74 \]
Since \( 74 \leq 70 \) is **False**, this indicates that having 16 small tables exceeds the fire code limit.
Therefore, the maximum number of small tables that can be in the cafeteria without violating the fire code is **15**.