A florist is creating 10 centerpieces for the tables at a wedding reception.Roses cost $2.50 each, lilies cost $8 each, and irises cost $4 each.The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined.
Write a system of linear equations that represents the situation.

A) $\left\{ \begin{array} { l l }
2.5 r - 8 l - 4 i & = 300 \
- r - 2 l - 2 i & = 0 \
r - l - i & = 120
\end{array} \right.$
B) $\left\{ \begin{array} { l l }
2.5 r + 8 l + 4 i & = 300 \
r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
C) $\left\{ \begin{array} { l l }
2.5 r + 8 l + 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
D) $\left\{ \begin{array} { l l }
2.5 r - 8 l + 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
E) $\left\{ \begin{array} { l l }
2.5 r + 8 l - 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$

Question

A florist is creating 10 centerpieces for the tables at a wedding reception.Roses cost $2.50 each, lilies cost $8 each, and irises cost $4 each.The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined.  
Write a system of linear equations that represents the situation.
 
A) $\left\{ \begin{array} { l l } 
2.5 r - 8 l - 4 i & = 300 \
- r - 2 l - 2 i & = 0 \
r - l - i & = 120
\end{array} \right.$
B)  $\left\{ \begin{array} { l l } 
2.5 r + 8 l + 4 i & = 300 \
r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
C)  $\left\{ \begin{array} { l l } 
2.5 r + 8 l + 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
D)  $\left\{ \begin{array} { l l } 
2.5 r - 8 l + 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$
E)  $\left\{ \begin{array} { l l } 
2.5 r + 8 l - 4 i & = 300 \
- r + 2 l + 2 i & = 0 \
r + l + i & = 120
\end{array} \right.$

Quizplus · Accepted Answer

The correct system of equations should reflect the cost of each type of flower, the relationship between the number of roses and the combined number of lilies and irises, and the total number of flowers per centerpiece. Option C correctly represents these conditions: the first equation accounts for the total cost of flowers for all centerpieces ($300), the second equation represents the condition that there are twice as many roses as the number of lilies and irises combined (with a sign correction for the roses), and the third equation ensures that each centerpiece contains a total of 12 flowers.

A Florist Is Creating 10 Centerpieces for the Tables at a Wedding