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 is: 1. The total cost equation, where the cost of roses ($2.50 each), lilies ($8 each), and irises ($4 each) multiplied by their respective quantities (r, l, i) equals the total budget ($300). This is represented as $2.5r + 8l + 4i = 300$.2. The relationship between the number of flowers, where there are twice as many roses as the number of lilies and irises combined. This can be represented as $r = 2(l + i)$ or equivalently $-r + 2l + 2i = 0$ when rearranged to fit the standard form of a linear equation.3. The total number of flowers in each centerpiece is 12, and since there are 10 centerpieces, the total number of flowers is $12 \times 10 = 120$. This gives the equation $r + l + i = 120$.

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