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Answer :
To find the cost of each jacket, we start with the information provided:
- The swim team ordered 36 jackets.
- The total cost for all the jackets was [tex]$1,116.
We need to find out how much each jacket costs. We can represent the cost of each jacket as \( c \).
The equation to find \( c \) is:
\[ 36 \cdot c = 1116 \]
This equation states that the total cost (1,116) is equal to the number of jackets (36) multiplied by the cost per jacket (\( c \)).
To solve for \( c \), you divide both sides of the equation by 36:
\[ c = \frac{1116}{36} \]
Performing the division gives:
\[ c = 31 \]
Thus, each jacket costs $[/tex]31.
Next, let's identify which of the given equations represent the problem correctly:
A. [tex]\( 1116 \cdot c = 36 \)[/tex] - This is not correct because it multiplies the total cost by the cost per jacket, which doesn't make sense in this context.
B. [tex]\( c = 1116 \cdot 36 \)[/tex] - This is not correct because it suggests multiplying the total cost by the number of jackets, which is incorrect.
C. [tex]\( 36 \cdot c = 1116 \)[/tex] - This is correct. It accurately expresses that 36 jackets at [tex]\( c \)[/tex] dollars each equal $1,116.
D. [tex]\( 1116 + 36 = c \)[/tex] - Not correct, as it incorrectly adds the total cost and the number of jackets.
E. [tex]\( 1116 + c = 36 \)[/tex] - Not correct, as it incorrectly suggests that adding the cost per jacket to the total cost equals the number of jackets.
Therefore, the correct equation from the options given is:
- C: [tex]\( 36 \cdot c = 1116 \)[/tex]
- The swim team ordered 36 jackets.
- The total cost for all the jackets was [tex]$1,116.
We need to find out how much each jacket costs. We can represent the cost of each jacket as \( c \).
The equation to find \( c \) is:
\[ 36 \cdot c = 1116 \]
This equation states that the total cost (1,116) is equal to the number of jackets (36) multiplied by the cost per jacket (\( c \)).
To solve for \( c \), you divide both sides of the equation by 36:
\[ c = \frac{1116}{36} \]
Performing the division gives:
\[ c = 31 \]
Thus, each jacket costs $[/tex]31.
Next, let's identify which of the given equations represent the problem correctly:
A. [tex]\( 1116 \cdot c = 36 \)[/tex] - This is not correct because it multiplies the total cost by the cost per jacket, which doesn't make sense in this context.
B. [tex]\( c = 1116 \cdot 36 \)[/tex] - This is not correct because it suggests multiplying the total cost by the number of jackets, which is incorrect.
C. [tex]\( 36 \cdot c = 1116 \)[/tex] - This is correct. It accurately expresses that 36 jackets at [tex]\( c \)[/tex] dollars each equal $1,116.
D. [tex]\( 1116 + 36 = c \)[/tex] - Not correct, as it incorrectly adds the total cost and the number of jackets.
E. [tex]\( 1116 + c = 36 \)[/tex] - Not correct, as it incorrectly suggests that adding the cost per jacket to the total cost equals the number of jackets.
Therefore, the correct equation from the options given is:
- C: [tex]\( 36 \cdot c = 1116 \)[/tex]
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