To determine which system of equations represents the situation accurately, we need to translate the given information into mathematical equations. We are given the costs of three different bouquets:
1. A bouquet with 6 roses, 3 lilies, and 2 carnations costs \$26.75.
2. A bouquet with 3 roses, 4 lilies, and 5 carnations costs \$25.50.
3. A bouquet with 1 rose, 1 lily, and 1 carnation costs \$6.75.
We need to represent these facts with a system of linear equations where \( r \) represents the cost of one rose, \( l \) represents the cost of one lily, and \( c \) represents the cost of one carnation.
Let's write down the equations for each bouquet:
1. For the first bouquet:
[tex]\[ 6r + 3l + 2c = 26.75 \][/tex]
2. For the second bouquet:
[tex]\[ 3r + 4l + 5c = 25.50 \][/tex]
3. For the third bouquet:
[tex]\[ r + l + c = 6.75 \][/tex]
Now we compare these equations to the given choices:
A.
[tex]\[
6r + 3l + 2c = 25.50 \\
3r + 4l + 5c = 26.75 \\
3r = 6.75
\][/tex]
B.
[tex]\[
\begin{aligned}
6r + 3l + 2c & = 26.75 \\
3r + 4l + 5c & = 25.50 \\
r + l + c & = 6.75
\end{aligned}
\][/tex]
C.
[tex]\[
6r + 3l + 2c = 25.50 \\
3r + 4l + 5c = 26.75 \\
r + l + c = 6.75
\][/tex]
D.
[tex]\[
\begin{aligned}
6r + 3l + 2c & = 26.75 \\
3r + 4l + 5c & = 25.50 \\
3r & = 6.75
\end{aligned}
\][/tex]
Comparing these, we see that the correct system matches the equations we wrote down:
B.
[tex]\[
\begin{aligned}
6r + 3l + 2c & = 26.75 \\
3r + 4l + 5c & = 25.50 \\
r + l + c & = 6.75
\end{aligned}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
