Question

charlie received a gift card of $100 for a pizza restaurant. the restaurant charges $15 per pizza. lucy received a gift card of $70 for a different pizza restaurant. the restaurant charges $10 per pizza. let x be the number of pizzas purchased. (a) for each card, write an expression for the amount of money left on the card after purchasing x pizzas. amount of money left on charlies card (in dollars) = \square amount of money left on lucys card (in dollars) = \square (b) write an equation to show when the two cards would have the same amount of money left on them. \square

Explanation:

Step1: Analyze Charlie's Card

Charlie has a $100 gift card, and each pizza costs $15. The money left is initial amount minus total cost for \( x \) pizzas. Total cost for \( x \) pizzas is \( 15x \). So, money left: \( 100 - 15x \).

Step2: Analyze Lucy's Card

Lucy has a $70 gift card, and each pizza costs $10. Total cost for \( x \) pizzas is \( 10x \). Money left: \( 70 - 10x \).

Step3: Set Equations Equal (Part b)

To find when they have the same money left, set Charlie's remaining money equal to Lucy's: \( 100 - 15x = 70 - 10x \).

Answer:

(a) Amount of money left on Charlie's card (in dollars) = \( 100 - 15x \)
Amount of money left on Lucy's card (in dollars) = \( 70 - 10x \)
(b) Equation: \( 100 - 15x = 70 - 10x \)