Question

mario sold concessions during the hockey tournament at the high school. he sold bottled water for $2.50 each and hamburgers for $5.50 each. by the end of the tournament, marios sold 350 items for a total of $1,325. which statements about the concession sales are true? check all that apply.

• the variable x could represent the number of bottles of water sold.
• the variable x could represent the total sales amount for the bottled water.
• the variable y could represent the total sales amount for the hamburgers.
• the variable y could represent the number of hamburgers sold.
• the system of equations that could represent the concession sales is

\\(2.50x + 5.50y = 1,325\\)
\\(x + y = 350\\)

• the system of equations that could represent this situation is

\\(x + y = 1,325\\)

Explanation:

Define the variables

Using the Variable Identification knowledge point

$$
LATEXBLOCK0
$$

Translate the total items sold

Using the System of Equations Translation knowledge point

$$ x + y = 350 $$

Translate the total sales revenue

Using the System of Equations Translation knowledge point

$$ 2.50x + 5.50y = 1,325 $$

Evaluate the given statements

Using the Variable Identification and System of Equations Translation knowledge points

• "The variable \(x\) could represent the number of bottles of water sold." (True, matches our definition of \(x\))
• "The variable \(x\) could represent the total sales amount for the bottled water." (False, the total sales amount for water is \(2.50x\))
• "The variable \(y\) could represent the total sales amount for the hamburgers." (False, the total sales amount for hamburgers is \(5.50y\))
• "The variable \(y\) could represent the number of hamburgers sold." (True, matches our definition of \(y\))
• "The system of equations that could represent the concession sales is \(2.50x + 5.50y = 1,325\) and \(x + y = 350\)." (True, matches our derived system)
• "The system of equations that could represent this situation is \(x + y = 1,325\) ..." (False, \(x + y\) represents the total number of items, which is \(350\))

Answer:

• The variable x could represent the number of bottles of water sold. (Correct answer)
• The variable x could represent the total sales amount for the bottled water.
• The variable y could represent the total sales amount for the hamburgers.
• The variable y could represent the number of hamburgers sold. (Correct answer)
• **The system of equations that could represent the concession sales is

\(2.50x + 5.50y = 1,325\)
\(x + y = 350\) (Correct answer)**

• The system of equations that could represent this situation is

\(x + y = 1,325\)
...