Question

Three friends went to the fair. Michelle ate three hot dogs, one pretzel, and two snow cones. She spent $25. Amanda ate two hot dogs, three pretzels, and three snow cones. She spent $30. Lucas ate two hot dogs, two pretzels, and four snow cones. He spent $25. Which system of equations matches the friends' night at the fair?

Answer 1

3x + y + 2z = 25

2x + 3y + 3z = 30

2x + 2y + 4z = 25

Explanation:

Let x, y and z represent the price ( in dollars ) of each hot dog, each pretzel and each snow cones respectively,

So, Price of 3 hot dogs, 1 pretzel, and 2 snow cones = 3x + y + 2z,

Price of 2 hot dogs, 3 pretzels, and 3 snow cones = 2x + 3y + 3z

And, price of 2 hot dogs, 2 pretzels, and 4 snow cones = 2x + 2y + 4z

According to the question,

3x + y + 2z = 25

2x + 3y + 3z = 30

2x + 2y + 4z = 25

Which is the required system of equations.

Answer 2

The system of equations is

`3x+y+2z=25`

`2x+3y+3z=30`

`2x+2y+4z=25`

Explanation:

Let

x ----> the cost of one hot dog

y ----> the cost of one pretzel

z ---> the cost of one snow cones

we know that

The system of equations that represent this situation is

Michelle

`3x+y+2z=25` -----> equation A

Amanda

`2x+3y+3z=30` -----> equation B

Lucas

`2x+2y+4z=25` -----> equation C