Question

the food for lucias quinceañera costs $18.50 per person. lucias abuela helped with the cooking, so the caterers gave a $50 discount. the equation, $y = 18.5x - 50$ can be used to find the total cost, including the discount.
what do the variables $x$ and $y$ represent? complete each statement.
the variable? represents the number of guests.
the variable $x$ represents the total cost, including the discount.
$y$

Explanation:

To determine what \( x \) and \( y \) represent, we analyze the equation \( y = 18.5x - 50 \). The cost per person is $18.50, so the total cost before discount would be LXI3 (number of people). The discount is $50, so we subtract that from the total cost before discount to get the final total cost.

• The term \( 18.5x \) suggests that \( x \) is the number of people (guests) because we multiply the cost per person by the number of people.
• The variable \( y \) is defined as the total cost including the discount, so \( y \) represents the total cost.

For the first blank (representing the number of guests), since \( x \) is multiplied by the cost per person, \( x \) must be the number of guests. For the second blank (representing the total cost), \( y \) is the result of the equation, which is the total cost after the discount.

Answer:

The variable \( \boldsymbol{x} \) represents the number of guests.
The variable \( \boldsymbol{y} \) represents the total cost, including the discount.