Sara, Jennifer, and Katrina bought snacks for a sleepover. Sara bought 4 bags of chips, 4 sodas, and 6 candies, for a total of $21.00. Jennifer bought 3 bags of chips, 2 sodas, and 10 candies, for a total of $20.88. Katrina bought 2 bags of chips, 3 sodas, and 4 candies, for a total of $13.17. Let x represent the number of bags of chips, y represent the number of sodas, and z represent the number of candies purchased. Create a system of three linear equations in three variables based on this description. Which of the following equations is part of the system?(1 point)

Question

Responses

4x+4y+6z=21
4
𝑥
+
4
𝑦
+
6
𝑧
=
21
4 x plus 4 y plus 6 z equals 21

4x+4y+6z=20.88
4
𝑥
+
4
𝑦
+
6
𝑧
=
20.88
4 x plus 4 y plus 6 z equals 20.88

3x+2y+10z=21
3
𝑥
+
2
𝑦
+
10
𝑧
=
21
3 x plus 2 y plus 10 z equals 21

x+3y+4z=13.17

Answer 1

To create a system of linear equations based on the purchases made by Sara, Jennifer, and Katrina, we will define the variables as follows:

• \( x \) = the price of one bag of chips
• \( y \) = the price of one soda
• \( z \) = the price of one candy

Now, let's analyze the purchases:

1. Sara's Purchase:

   • 4 bags of chips, 4 sodas, and 6 candies for a total of $21.00: \[ 4x + 4y + 6z = 21 \]

2. Jennifer's Purchase:

   • 3 bags of chips, 2 sodas, and 10 candies for a total of $20.88: \[ 3x + 2y + 10z = 20.88 \]

3. Katrina's Purchase:

   • 2 bags of chips, 3 sodas, and 4 candies for a total of $13.17: \[ 2x + 3y + 4z = 13.17 \]

Thus, the correct system of equations based on the information given is:

1. \( 4x + 4y + 6z = 21 \)
2. \( 3x + 2y + 10z = 20.88 \)
3. \( 2x + 3y + 4z = 13.17 \)

From the provided options, the first equation \( 4x + 4y + 6z = 21 \) is indeed part of the system. Therefore, the equation that belongs to the system is:

4x + 4y + 6z = 21