Answer :
To determine the correct expressions for the total number of furniture legs in aisle 2, let's carefully analyze each option considering there are [tex]\( t \)[/tex] tables, [tex]\( c \)[/tex] chairs, and [tex]\( s \)[/tex] stools, where:
- Each table has 4 legs.
- Each chair has 4 legs.
- Each stool has 3 legs.
Let's review each expression one by one:
1. [tex]\( 4t + 4c + 3s \)[/tex]:
- This correctly accounts for the legs of all furniture pieces: 4 legs per table ([tex]\( t \)[/tex]), 4 legs per chair ([tex]\( c \)[/tex]), and 3 legs per stool ([tex]\( s \)[/tex]). This is a correct expression.
2. [tex]\( 4t + 4c + 4s \)[/tex]:
- This expression incorrectly assigns 4 legs to each stool. Since stools have 3 legs, this is incorrect.
3. [tex]\( 4(t + c) + 3s \)[/tex]:
- This expression can be simplified to [tex]\( 4t + 4c + 3s \)[/tex]. It correctly accounts for the legs of tables and chairs combined ([tex]\( 4(t + c) \)[/tex]), plus the legs of the stools ([tex]\( 3s \)[/tex]). This is a correct expression.
4. [tex]\( 4(t + c + s) \)[/tex]:
- This expression incorrectly assumes all items have 4 legs each. Since stools have 3 legs, this is incorrect.
5. [tex]\( t + c + s \)[/tex]:
- This ignores the number of legs on each piece of furniture and just sums the counts of the items. This is incorrect.
6. [tex]\( t + c + 3s \)[/tex]:
- This expression correctly accounts for the legs on stools but completely ignores the legs on tables and chairs. This is incorrect.
The correct expressions for the total number of furniture legs in aisle 2 are:
- [tex]\( 4t + 4c + 3s \)[/tex]
- [tex]\( 4(t + c) + 3s \)[/tex]
So, the correct answers are:
- [tex]\( 4t + 4c + 3s \)[/tex]
- [tex]\( 4(t + c) + 3s \)[/tex]
- Each table has 4 legs.
- Each chair has 4 legs.
- Each stool has 3 legs.
Let's review each expression one by one:
1. [tex]\( 4t + 4c + 3s \)[/tex]:
- This correctly accounts for the legs of all furniture pieces: 4 legs per table ([tex]\( t \)[/tex]), 4 legs per chair ([tex]\( c \)[/tex]), and 3 legs per stool ([tex]\( s \)[/tex]). This is a correct expression.
2. [tex]\( 4t + 4c + 4s \)[/tex]:
- This expression incorrectly assigns 4 legs to each stool. Since stools have 3 legs, this is incorrect.
3. [tex]\( 4(t + c) + 3s \)[/tex]:
- This expression can be simplified to [tex]\( 4t + 4c + 3s \)[/tex]. It correctly accounts for the legs of tables and chairs combined ([tex]\( 4(t + c) \)[/tex]), plus the legs of the stools ([tex]\( 3s \)[/tex]). This is a correct expression.
4. [tex]\( 4(t + c + s) \)[/tex]:
- This expression incorrectly assumes all items have 4 legs each. Since stools have 3 legs, this is incorrect.
5. [tex]\( t + c + s \)[/tex]:
- This ignores the number of legs on each piece of furniture and just sums the counts of the items. This is incorrect.
6. [tex]\( t + c + 3s \)[/tex]:
- This expression correctly accounts for the legs on stools but completely ignores the legs on tables and chairs. This is incorrect.
The correct expressions for the total number of furniture legs in aisle 2 are:
- [tex]\( 4t + 4c + 3s \)[/tex]
- [tex]\( 4(t + c) + 3s \)[/tex]
So, the correct answers are:
- [tex]\( 4t + 4c + 3s \)[/tex]
- [tex]\( 4(t + c) + 3s \)[/tex]
