Question

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) Responses 4x+4y+6z=20.88 4 x plus 4 y plus 6 z equals 20.88 x+3y+4z=13.17 x plus 3 y plus 4 z equals 13.17 3x+2y+10z=21 3 x plus 2 y plus 10 z equals 21 4x+4y+6z=21

Answer 1

To set up the system of equations based on the purchases of Sara, Jennifer, and Katrina, we need to use the following variables:

• Let \( x \) be the price of a bag of chips.
• Let \( y \) be the price of a soda.
• Let \( z \) be the price of a candy.

We can create the following equations from the information given:

1. Sara's purchases:
   Sara bought 4 bags of chips, 4 sodas, and 6 candies, totaling $21.00.
   This can be expressed as:
   \[ 4x + 4y + 6z = 21 \]

2. Jennifer's purchases:
   Jennifer bought 3 bags of chips, 2 sodas, and 10 candies, totaling $20.88.
   This can be expressed as:
   \[ 3x + 2y + 10z = 20.88 \]

3. Katrina's purchases:
   Katrina bought 2 bags of chips, 3 sodas, and 4 candies, totaling $13.17.
   This can be expressed as:
   \[ 2x + 3y + 4z = 13.17 \]

Now we have the following system of equations:

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

From the options provided, the equation that is part of the system is:

• 4x + 4y + 6z = 21

This is the correct equation that corresponds to Sara's purchases.

So the answer is: \[ \boxed{4x + 4y + 6z = 21} \]