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:
\[
\boxed{4x + 4y + 6z = 21}
\]