Question

6 andrew bought 3 apple pies and 2 chocolate pies for $14.50. for $13 more, kyra bought 5 apple pies and 4 chocolate pies. which system of equations can be used to find the cost of an apple pie, a, and the cost of a chocolate pie, c?

f \\(\

$$\begin{cases} 3a + 2c = 14.50 \\\\ 5a + 4c = 27.50 \\end{cases}$$

\\)

g \\(\

$$\begin{cases} 3a + 2c = 14.50 \\\\ 5a + 4c = 13 \\end{cases}$$

\\)

h \\(\

$$\begin{cases} 2a + 3c = 14.50 \\\\ 4a + 5c = 27.50 \\end{cases}$$

\\)

j \\(\

$$\begin{cases} 2a + 3c = 13 \\\\ 4a + 5c = 14.50 \\end{cases}$$

\\)

Explanation:

Define variables and model Andrew's purchase

Using the Linear Function Modeling knowledge point

$$
LATEXBLOCK0
$$

Model Kyra's purchase

Using the Linear Function Modeling knowledge point

$$
LATEXBLOCK1
$$

Formulate the system of equations

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK2
$$

Verify the correct option

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK3
$$

Answer:

• **F \(

$$\begin{cases} 3a + 2c = 14.50 \\ 5a + 4c = 27.50 \end{cases}$$

\) (Correct answer)**

• G \(

$$\begin{cases} 3a + 2c = 14.50 \\ 5a + 4c = 13 \end{cases}$$

\)

• H \(

$$\begin{cases} 2a + 3c = 14.50 \\ 4a + 5c = 27.50 \end{cases}$$

\)

• J \(

$$\begin{cases} 2a + 3c = 13 \\ 4a + 5c = 14.50 \end{cases}$$

\)